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4
3
2
1
Grade 9
/ Literal expressions
49 exercises corrected
a
Reminders
(8 exercices)
Reminders: simple distributivity
(12 exercices)
Reminders: simple distributivity and factorization
(14 exercices)
Factoring
(11 exercices)
ChingQuizz
:
3
exercises
a
v
ailable
for
Quizz
assessmen
t
:
1.
R
eminders
E.3588
Consider
the
follo
wing
calculation
program
:
Cho
ose
a
starting
n
um
b
er.
A
dd
1
.
Calculate
the
square
of
the
result
obtained.
Subtract
the
square
of
the
starting
n
um
b
er
from
it.
W
rite
do
wn
the
final
result.
1
Chec
k
that
when
the
starting
n
um
b
er
is
1
,
the
final
result
is
3
.
2
When
the
starting
n
um
b
er
is
2
,
what
is
the
final
result?
3
With
the
starting
n
um
b
er
b
eing
x
,
express
the
final
result
in
terms
of
x
.
E.3587
1
Determine,
for
eac
h
of
the
ab
o
v
e
segmen
ts,
an
expression
for
their
lengths
as
a
function
of
x
.
2
Giv
e
the
length
of
eac
h
of
these
segmen
ts
when
x
=
5
.
E.3694
Studen
ts
in
3
ième
w
ere
ask
ed
the
follo
wing
question
:
ˇEst
it
true
that,
for
an
y
v
alue
of
the
n
um
b
er
x
,
w
e
ha
v
e
:
5
x
2
−
10
x
+
2
=
7
x
−
4
ı
Lea
replied
:
ˇ
Y
es,
that
is
true.
Indeed,
if
w
e
replace
x
with
3
,
w
e
ha
v
e
:
5
×
3
2
−
10
×
3+2
=
17
and
7
×
3
−
4
=
17
ı
Myriam
replied
:
ˇNo,
this
is
not
true.
In
fact,
if
w
e
re-
place
x
with
0
,
w
e
ha
v
e
:
5
×
0
2
−
10
×
0+2
=
2
and
7
×
0
−
4
=
−
4
ı
One
of
these
t
w
o
studen
ts
has
giv
en
an
argumen
t
that
cor-
rectly
answ
ers
the
question
p
osed
in
the
exercise.
State
whic
h
one
b
y
explaining
wh
y
.
E.3762
The
follo
wing
calculation
pro-
gram
is
giv
en
:
Cho
ose
a
n
um
b
er.
Multiply
that
n
um
b
er
b
y
3
.
A
dd
the
square
of
the
c
hosen
n
um
b
er.
Multiply
b
y
2
.
W
rite
the
result.
1
Sho
w
that,
if
w
e
c
ho
ose
the
n
um
b
er
10
,
the
result
ob-
tained
is
260
.
2
Calculate
the
exact
v
alue
of
the
result
obtained
when
:
The
n
um
b
er
c
hosen
is
−
5
;
the
c
hosen
n
um
b
er
is
2
5
.
E.3603
F
or
eac
h
of
the
t
w
o
cases
b
elo
w
find
the
literal
expression
that
w
as
en
tered
in
to
the
calculator
to
obtain
the
follo
wing
table
:
1
V
aleur
de
x
Résultat
affic
hé
1
7
2
12
3
17
4
22
2
V
aleur
de
x
Résultat
affic
hé
1
20
2
13
3
6
4
-1
E.3638
W
e
consider
the
follo
wing
three
lit-
eral
expressions
:
A
=
8
x
−
8
;
B
=
3(3
x
−
4)
−
x
+4
;
C
=
(
x
−
1)(2
x
+4)
1
a
Ev
aluate
these
three
expressions
for
the
differen
t
v
al-
ues
of
x
prop
osed
:
A
B
C
x
=
1
x
=
2
x
=
0
b
Can
w
e
sa
y
that
the
expressions
A
and
B
are
equal?
Can
w
e
sa
y
that
the
expressions
B
and
C
are
equal?
2
a
Giv
e
the
expanded
and
reduced
form
of
the
expres-
sions
A
and
B
.
b
What
can
w
e
conclude
ab
out
the
expressions
A
and
B
?
E.688
Determine
the
reduced
expression
of
eac
h
of
the
follo
wing
expressions
:
A
=
x
+
3
4
−
3
x
−
2
4
;
B
=
2
x
+
5
3
+
x
−
2
2
h
ttps:/
/c
hingmath.fr
quizzChap/1044
chapExoCorrec/3588
sacados/3588
chapExoCorrec/3587
sacados/3587
A
B
x
7
cm
D
C
x
12
cm
E
F
x
2
x
1
cm
1
cm
chapExoCorrec/3694
sacados/3694
France Septembre 2008
chapExoCorrec/3762
sacados/3762
chapExoCorrec/3603
sacados/3603
chapExoCorrec/3638
sacados/3638
chapExoCorrec/688
sacados/688
E.2228
Giv
e
eac
h
of
the
expressions
b
elo
w
in
their
simplest
form
:
a
3
x
−
2
5
−
−
7
−
2
x
5
b
2
x
−
1
3
+
x
+
1
4
2.
R
eminders
:
simple
distributivity
E.9154
Dev
elop
and
simplify
expressions
:
a
3
×
(
x
+
2)
b
5
×
(2
x
−
1)
e
3
×
(4
x
−
1)
E.
3604
Expand
and
reduce
eac
h
of
the
follo
wing
expressions
:
a
2
x
−
2
+
3
x
+
2
b
4
1
−
x
+
3
x
+
1
E.9200
Expand
and
then
reduce
eac
h
of
the
follo
wing
expressions
:
E.11543
Expand
and
then
reduce
eac
h
of
the
follo
wing
expressions
:
E.
11372
Dev
elop
and
simplify
expressions
:
a
2
×
(6
+
x
+
2)
b
3
×
5
+
2
x
+
3
x
E.10808
Expand
and
reduce
the
follo
wing
expression
:
A
=
3
2
x
−
5
−
4
×
(3
x
−
2
E.9195
Expand
and
reduce
the
follo
wing
expressions
:
a
3(2
x
−
1)
−
3(5
−
2
x
)
b
2(1
−
x
)
−
6(
x
+
2)
E.9196
Expand
and
then
reduce
eac
h
of
the
follo
wing
expressions
:
E.2204
Expand
and
reduce
the
follo
wing
expressions
:
a
−
(
x
2
−
3
x
+
2)
+
2(2
x
+
1)
b
x
(2
x
−
1)
−
(
x
2
+11
x
+2)
c
2
x
×
(8
−
x
)
−
5
x
×
(
x
+1)
E.11369
Expand
and
simplify
the
expres-
sions
:
a
(2
x
+
1)
×
5
+
2
c
2
×
(4
+
x
+
5)
E.11370
Expand
and
simplify
the
expres-
sions
:
a
2
×
(
x
−
1)
+
8
×
(3
x
+
4)
b
3
×
(
x
+
2)
+
2
×
(3
x
−
1)
E.11371
Expand
and
then
reduce
eac
h
of
the
follo
wing
expressions
:
3.
R
eminders
:
simple
distributivity
and
factorization
E.9197
F
actor
the
follo
wing
expressions
:
a
3
x
+
6
b
16
x
−
4
c
3
x
+
9
E.5205
F
actorize
the
expressions
b
elo
w
(we
wil
l
b
e
le
d
to
r
eve
al
a
factor
c
ommon
to
the
terms
of
the
sum)
:
a
10
x
−
15
b
14
x
−
12
c
−
6
x
−
4
E.11493
F
actorize
the
expressions
b
elo
w
(we
wil
l
b
e
le
d
to
r
eve
al
a
factor
c
ommon
to
the
terms
of
the
sum)
:
a
6
x
+
4
b
14
−
21
x
c
15
x
−
10
E.11544
F
actor
the
follo
wing
expressions
using
distributivit
y
:
a
4
x
+
6
b
x
2
+
3
x
E.9202
F
actor
the
follo
wing
algebraic
ex-
pressions
using
distributivit
y
:
a
3
x
+
5
x
b
4
x
2
+
3
x
c
x
2
+
3
x
E.10740
F
actorize
the
expressions
b
elo
w
(we
wil
l
b
e
le
d
to
r
eve
al
a
factor
c
ommon
to
the
terms
of
the
sum)
:
a
5
x
2
+
7
x
b
10
x
2
+
7
x
c
5
x
+
3
x
2
E.10811
F
actor
the
follo
wing
expressions
:
a
7
x
+
7
x
2
b
8
x
2
+
6
x
c
6
x
+
15
x
2
E.11492
F
actor
the
follo
wing
algebraic
ex-
pressions
using
distributivit
y
:
a
x
2
x
+
3)
+
5
x
2
b
10
x
+
x
(
x
−
4)
E.10741
F
actor
then
reduce
eac
h
of
the
fac-
tors
of
the
resulting
expression
:
a
5
×
x
+
2
+
5
×
3
x
+
1
b
x
×
4
x
−
2
+
x
×
x
+
5
E.10742
F
actor
then
reduce
eac
h
of
the
fac-
tors
of
the
resulting
expression
:
a
x
x
−
2
−
x
7
x
−
5
b
x
2
3
x
+
2
−
x
2
×
3
−
x
E.10958
F
actor
the
follo
wing
expressions
:
a
x
3
x
+
2
+
x
5
−
x
b
x
2
x
+
1
−
x
2
E.10960
F
actor
the
follo
wing
expressions
:
a
5
x
2
+
3
x
−
4
x
×
y
b
6
x
4
y
+
1
+
x
5
−
y
h
ttps:/
/c
hingmath.fr
chapExoCorrec/2228
sacados/2228
chapExoCorrec/9154
sacados/9154
chapExoCorrec/3604
sacados/3604
chapExoCorrec/9200
sacados/9200
chapExoCorrec/11543
sacados/11543
chapExoCorrec/11372
sacados/11372
chapExoCorrec/10808
sacados/10808
chapExoCorrec/9195
sacados/9195
chapExoCorrec/9196
sacados/9196
chapExoCorrec/2204
sacados/2204
chapExoCorrec/11369
sacados/11369
chapExoCorrec/11370
sacados/11370
chapExoCorrec/11371
sacados/11371
chapExoCorrec/9197
sacados/9197
chapExoCorrec/5205
sacados/5205
chapExoCorrec/11493
sacados/11493
chapExoCorrec/11544
sacados/11544
chapExoCorrec/9202
sacados/9202
chapExoCorrec/10740
sacados/10740
chapExoCorrec/10811
sacados/10811
chapExoCorrec/11492
sacados/11492
chapExoCorrec/10741
sacados/10741
chapExoCorrec/10742
sacados/10742
chapExoCorrec/10958
sacados/10958
chapExoCorrec/10960
sacados/10960
E.10790
F
actor
ˇ
to
the
maxim
um
ı
the
fol-
lo
wing
expressions
:
a
10
x
+
5
x
×
2
x
+
1
b
15
x
4
×
y
2
+
3
x
2
×
y
5
E.10826
Determine
the
factorized
form
of
eac
h
of
the
follo
wing
expressions
:
a
12
x
2
+
15
x
2
x
+
3
b
5
x
2
+
3
x
5
×
y
2
4.
F
actoring
E.686
W
e
are
going
to
factor
the
follo
wing
expressions
:
a
(2
x
−
1)(3
x
+
1)
+
(2
x
−
1)(5
−
2
x
)
c
(
x
−
3)(2
x
+
2)
+
(
x
−
3)
x
d
2(
x
−
1)
−
(
x
−
1)(3
x
+
3)
1
Eac
h
of
the
ab
o
v
e
expressions
is
a
sum
(or
a
differ
enc
e)
where
eac
h
of
its
terms
is
a
pro
duct.
In
eac
h
expression,
underline
the
common
factor
of
its
t
w
o
terms.
2
Noting
k
as
the
common
factor
and
a
,
b
as
the
other
t
w
o
factors,
complete
the
table
b
elo
w
:
k
a
b
a
b
c
3
F
actor
eac
h
of
these
expressions.
Definition
:
The
distributiv
e
prop
ert
y
of
m
ultiplication
o
v
er
addition
giv
es
the
t
w
o
factorization
form
ulas
:
k
·
a
+
k
·
b
=
k
×
(
a
+
b
)
;
k
·
a
−
k
·
b
=
k
×
(
a
−
b
)
E.10961
F
actor
the
follo
wing
expressions
:
a
(2
x
+
1)
×
2
+
(2
x
+
1)
×
x
2
b
(5
−
2
x
)
×
2
+
(5
−
2
x
)
×
x
Hin
t
:
b
efore
y
ou
start
factoring,
y
ou
can
underline
the
common
factor
presen
t
in
eac
h
term
of
the
expression.
E.10959
F
actor
the
follo
wing
expressions
:
a
(4
x
+
3)(2
−
3
x
)
−
(2
−
3
x
)(
x
−
1)
b
(
x
+
1)
2
+
(
x
+
1)(2
x
−
3)
E.9203
F
actor
the
follo
wing
expressions
:
a
4(5
x
+
2)
+
2
x
(5
x
+
2)
b
(3
x
+
2)2
x
+
2
x
(2
−
x
)
Hin
t
:
Before
starting
to
factor,
y
ou
can
underline
the
com-
mon
factor
presen
t
in
eac
h
term
of
the
expression.
E.705
F
actor
the
follo
wing
expressions
:
a
5
x
(1
−
x
)
+
(5
x
+
2)(1
−
x
)
b
(3
x
−
2)(
x
+
1)
+
(3
x
−
2)(1
−
x
)
Indication
:
b
efore
starting
the
factorization,
w
e
can
un-
derline
the
common
factor
presen
t
in
eac
h
of
the
terms
of
the
expression.
E.704
F
actor
the
follo
wing
expressions
:
a
3(
x
+
2)
+
(
x
+
1)(
x
+
2)
b
(2
−
x
)(
x
+1)
−
(2
−
x
)
E.10962
F
actor
the
follo
wing
expressions
:
a
(3
x
−
4)(3
−
2
x
)
−
(3
−
2
x
)
b
(2
x
+1)(5
x
+1)
−
x
(2
x
+1)
E.10964
F
actor
the
follo
wing
expressions
:
a
(2
x
−
1)(
x
+
1)
+
(
x
+
5)(
x
+
1)
b
3
x
2
x
+
5
−
2
x
+
5
x
+
5
E.685
F
actorize
algebraic
expressions
:
a
(1
−
3
x
)(2
+
x
)
+
(1
−
3
x
)(5
−
2
x
)
b
(2
+
3
x
)(
x
−
1)
−
(
x
+
1)(3
x
+
2)
E.9204
F
actor
the
follo
wing
expressions
a
(
x
+
1)
2
+
(
x
+
1)(5
x
−
4)
b
(9
x
+
1)
2
+
(9
x
+
1)(1
−
x
)
E.10963
F
actor
the
follo
wing
expressions
a
(2
x
+
3)
2
+
2
x
+
3
b
5
x
+
3
2
−
5
x
−
3
5.
Unclassifie
d
exer
cises
E.6354
Alexandre
on
building
a
house
of
cards.
He
succeeded
in
building
a
3
-storey
castle.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/10790
sacados/10790
chapExoCorrec/10826
sacados/10826
chapExoCorrec/686
sacados/686
chapExoCorrec/10961
sacados/10961
chapExoCorrec/10959
sacados/10959
chapExoCorrec/9203
sacados/9203
chapExoCorrec/705
sacados/705
chapExoCorrec/704
sacados/704
chapExoCorrec/10962
sacados/10962
chapExoCorrec/10964
sacados/10964
chapExoCorrec/685
sacados/685
chapExoCorrec/9204
sacados/9204
chapExoCorrec/10963
sacados/10963
chapExoCorrec/6354
sacados/6354
1
étage
2
étage
3
étage
Let
n
b
e
a
strictly
p
ositiv
e
in
teger.
T
o
find
out
the
n
um
b
er
of
cards
needed
to
build
the
castle
with
n
flo
ors,
the
follo
wing
three
expressions
are
prop
osed
:
a
5
n
−
3
b
3
2
n
2
+
1
2
n
c
2
n
2
−
n
+
1
T
w
o
of
these
expressions
are
not
correct.
Whic
h
t
w
o?
E.
8978
The
figure
b
elo
w
giv
es
a
sc
hematic
of
a
calculation
program.
1
If
the
starting
n
um
b
er
is
1
,
sho
w
that
the
result
is
−
15
.
2
If
w
e
c
ho
ose
an
y
n
um
b
er
x
as
the
starting
n
um
b
er,
whic
h
of
the
follo
wing
expressions
giv
es
the
result
obtained
b
y
the
calculation
program?
Justify
.
A
=
x
2
−
5
×
3
x
+2
B
=(2
x
−
5)(3
x
+2)
C
=2
x
−
5
×
3
x
+2
3
Lily
claims
that
the
expression
:
D
=
(3
x
+2)
2
−
(
x
+7)(3
x
+2)
giv
es
the
same
results
as
the
expression
B
for
all
v
alues
of
x
.
Is
Lily’s
statemen
t
true?
Justify
.
E.8682
Here
are
t
w
o
calculation
pro-
grams
:
1
a
Sho
w
that,
if
w
e
c
ho
ose
the
n
um
b
er
5
,
the
result
of
the
program
A
is
29
.
b
What
is
the
result
of
the
program
B
if
w
e
c
ho
ose
the
n
um
b
er
5
?
2
If
w
e
name
x
the
c
hosen
n
um
b
er,
explain
wh
y
the
result
of
the
program
A
can
b
e
written
x
2
+4
.
3
What
is
the
result
of
the
program
B
if
w
e
name
x
the
c
hosen
n
um
b
er?
4
Are
the
follo
wing
statemen
ts
true
or
false?
Justify
the
answ
ers
and
write
the
steps
of
an
y
calculations
:
a
ˇ
If
w
e
c
ho
ose
the
n
um
b
er
2
3
,
the
result
of
the
program
B
is
58
9
.
ı
b
ˇ
If
w
e
c
ho
ose
an
in
teger,
the
result
of
the
program
B
is
an
o
dd
in
teger.
ı
c
ˇ
The
result
of
the
program
B
is
alw
a
ys
a
p
ositiv
e
n
um-
b
er.
ı
d
ˇ
F
or
the
same
c
hosen
in
teger,
the
results
of
the
pro-
grams
A
and
B
are
either
b
oth
ev
en-n
um
b
ered
in
tegers,
or
b
oth
in
tegers
impairs
ı
E.682
Reduce
expression
A
:
A
=
2
×
3
x
+1
4
−
1
−
x
2
h
ttps:/
/c
hingmath.fr
chapExoCorrec/8978
sacados/8978
Choisir un nombre
Calculer son triple
Calculer son double
Ajouter
2
Multiplier les deux nombres obtenus
Soustraire
5
chapExoCorrec/8682
sacados/8682
Brevet Antilles Guyanes Juin 2019
Programme A
Choisir un nombre
Soustraire 2
Multiplier par
4
Elever au carré
Ajouter les deux nombres
Programme B
•
Choisir un nombre
•
Calculer son carré
•
Ajouter
6
au résultat
chapExoCorrec/682
sacados/682
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