Activities 1

1.1)

Find the answers and take note of what the parentheses do to the calculation and the answer:

a)
7 × 4 + 3
b)
7 × (4 + 3)
c)
10 3 × 3
d)
(10 3) × 3
e)
5 × 8 + 4 × 9
f)
5 × (8 + 4) × 9
g)
20 + 3 × 7 4 × 2 + 9
h)
((20 + 3) × 7) 4 × (2 + 9)

a)
7 × 4 + 3
b)
7 × (4 + 3)
c)
10 3 × 3
d)
(10 3) × 3
e)
5 × 8 + 4 × 9
f)
5 × (8 + 4) × 9
g)
20 + 3 × 7 4 × 2 + 9
h)
((20 + 3) × 7) 4 × (2 + 9)

1.2)

Expand the parentheses and find the answers:

a)
(8 + 19) + (12 4)
b)
(4 + 13) + (3 + 26)
c)
(7 12) (9 16)
d)
(8 + 3) + (7 + 20)
e)
(10 + 8) + (5 3)
f)
(100 20) + (5 + (12))
g)
(6 5) (7 (14))
h)
(4 3) (9 (5))

a)
(8 + 19) + (12 4)
b)
(4 + 13) + (3 + 26)
c)
(7 12) (9 16)
d)
(8 + 3) + (7 + 20)
e)
(10 + 8) + (5 3)
f)
(100 20) + (5 + (12))
g)
(6 5) (7 (14))
h)
(4 3) (9 (5))

1.3)

Find the answers:

a)
3 1 × 3
b)
(3 1) × 3
c)
(4 2) × (2 + 5)
d)
2(3 + 2)
e)
14(2 + 1)
f)
3 × 2 + 4 × 2 3 × 5
g)
(3 + 4)(11 + 19)
h)
7(2 9)
i)
17 + 3(2 + 5) 2(1 + (8))

a)
3 1 × 3
b)
(3 1) × 3
c)
(4 2) × (2 + 5)
d)
2(3 + 2)
e)
14(2 + 1)
f)
3 × 2 + 4 × 2 3 × 5
g)
(3 + 4)(11 + 19)
h)
7(2 9)
i)
17 + 3(2 + 5) 2(1 + (8))

1.4)

Expand the expressions and simplify them as much as possible:

a)
2 ×(3 8 + 1 4)
b)
(5 6 2 9) × 3 5
c)
( 5 36 + 1 12) 2 9
d)
(7 6 2 9) ×(1 5 + 1 4)
e)
4 33(32 26)
f)
(29 19) 1 60
g)
(4 + 9 4) 4 5
h)
8 3 (9 5 + 7)

a)
2 ×(3 8 + 1 4)
b)
(5 6 2 9) × 3 5
c)
( 5 36 + 1 12) 2 9
d)
(7 6 2 9) ×(1 5 + 1 4)
e)
4 33(32 26)
f)
(29 19) 1 60
g)
(4 + 9 4) 4 5
h)
8 3 (9 5 + 7)

1.5)

Expand the expressions and simplify them as much as possible:

a)
3 (1 2 + 3 4)
b)
12 (1 3 + 1 4)
c)
24 (2 8 + 3 6)
d)
1 2 (5 9 + 24 10)
e)
4 (2 5 4 7)
f)
( 6 10 1 3) 5
g)
(4 1 2) 7
h)
(6 5 + 2) 8

a)
3 (1 2 + 3 4)
b)
12 (1 3 + 1 4)
c)
24 (2 8 + 3 6)
d)
1 2 (5 9 + 24 10)
e)
4 (2 5 4 7)
f)
( 6 10 1 3) 5
g)
(4 1 2) 7
h)
(6 5 + 2) 8

1.6)

Expand the expressions and simplify them if possible:

a)
2(3 + a)
b)
a(5 + b)
c)
1 3 (3 + b)
d)
(2 + a) 3 4
e)
b (2 3 + 1 3)
f)
3 8(a + b)
g)
(b 2b 9 ) 6
h)
8 3 (a 3 + b)

1.7)

Expand the parentheses and contract the resulting expressions:

a)
(x + 2)(y 2x)
b)
(2x2 a) (b a)
c)
(a + b)(a + b)
d)
(a b)(a b)
e)
(a b)(a + b)
f)
(x + y)(x + y)
g)
(x + y)(x + y)(x + y)
h)
2(a + 3b)(a + b)
i)
5(2a + b)(3a 2b)
j)
3(4x + 6y)(x + 2y)(3x + 5y)
k)
7 (2x2 + 3y) (2x + 5y)
l)
2 (6x2 + 2y2) (3x2 + y2)
m)
(a + b)(a + b)(a + b)(a + b)

1.8)

Expand the parentheses and contract the resulting expressions:

a)
x(x + 2) + (x + 2)(x + 1)
b)
(x + 4)(x + 5) 3x(5 + 2x)
c)
(3x 2)(5 + 2x) + (4x + 4)(6x + 1)
d)
(4x + 2)(3 + 2x) (9x + 1)(2x 3)
e)
(5 + 4x)(2 + 6x) (x 7)(3x 5)
f)
(5 + 4x)(2 + 6x) + (x 7)(3x 5)

a)
x(x + 2) + (x + 2)(x + 1)
b)
(x + 4)(x + 5) 3x(5 + 2x)
c)
(3x 2)(5 + 2x) + (4x + 4)(6x + 1)
d)
(4x + 2)(3 + 2x) (9x + 1)(2x 3)
e)
(5 + 4x)(2 + 6x) (x 7)(3x 5)
f)
(5 + 4x)(2 + 6x) + (x 7)(3x 5)

1.9)

Expand the parentheses and contract the resulting expressions:

a)
2(a + b)(3a + b) + 3(2a + b)(a b)
b)
7(4a 2b)(2a b) (a 4b)(2a b)
c)
4(2a b)(3a 2b) 3(5a (3) b)(a + b)
d)
(a + b)(2a 3b) 5(2a 2b)(6a + b) (3a 4b)
e)
(2a 5)(3b + 1) (4a + 3b 2)(a + b) + 5(3a + b)

a)
2(a + b)(3a + b) + 3(2a + b)(a b)
b)
7(4a 2b)(2a b) (a 4b)(2a b)
c)
4(2a b)(3a 2b) 3(5a (3) b)(a + b)
d)
(a + b)(2a 3b) 5(2a 2b)(6a + b)(3a 4b)
e)
(2a 5)(3b + 1) (4a + 3b 2)(a + b) + 5(3a + b)

1.10)

Expand the parentheses and contract the resulting expressions:

a)
2x + (3 + 4x)
b)
x + 2(x + 5)
c)
7x + 2(6x + 11 + 2x) + x
d)
5 + 3x + 2(x + 2) + 4x
e)
7 2x + 3(2x + 5) (2 + (7) + 3x)
f)
3x 2(x + 3)
g)
4x 3(2 x)
h)
x + 5 4(1 + 3x)

a)
2x + (3 + 4x)
b)
x + 2(x + 5)
c)
7x + 2(6x + 11 + 2x) + x
d)
5 + 3x + 2(x + 2) + 4x
e)
7 2x + 3(2x + 5) (2 + (7) + 3x)
f)
3x 2(x + 3)
g)
4x 3(2 x)
h)
x + 5 4(1 + 3x)

1.11)

Expand the parentheses and contract the resulting expressions:

a)
5x2 3x(2x 3)(4x + 2)
b)
7x + 3 5x(x + 2)(2x 1)
c)
x2 x + 2 + 3(2 3x)(5x + 3)
d)
x2 7x(2x + 3)(2x 3) (5x 3)
e)
2x(4x 5)(6x + 3) x(x + 4)(3x 1)
f)
(2x 3)(3x + 5) 3x(4x 2)(3x 2

a)
5x2 3x(2x 3)(4x + 2)
b)
7x + 3 5x(x + 2)(2x 1)
c)
x2 x + 2 + 3(2 3x)(5x + 3)
d)
x2 7x(2x + 3)(2x 3) (5x 3)
e)
2x(4x 5)(6x + 3) x(x + 4)(3x 1)
f)
(2x 3)(3x + 5) 3x(4x 2)(3x 2)

1.12)

Simplify the expressions as much as possible:

a)
2(4x + 5x) x(12 3)
b)
4x(2 + 3) 5x x(7 6)
c)
18y (15 9)y
d)
(9x + 4x) 2(20x + 6x)
e)
5x(x + 2x) (9 4)x
f)
(y + 5y)3y 4(15y 8y + 2y)
g)
y(3 + 8)(4 + 12) 5(6y 3y)
h)
8(11x 9x) 4 (12 16)

a)
2(4x + 5x) x(12 3)
b)
4x(2 + 3) 5x x(7 6)
c)
18y (15 9)y
d)
(9x + 4x) 2(20x + 6x)
e)
5x(x + 2x) (9 4)x
f)
(y + 5y)3y 4(15y 8y + 2y)
g)
y(3 + 8)(4 + 12) 5(6y 3y)
h)
8(11x 9x) 4 (12 16)

1.13)

Contract the expressions:

a)
a2 + 4(3a + b)(7a + 2b) + 3b2 (2 + 5b)
b)
ab + 3b 4 + 2(6a 3b) 4ab + (a + 2b)(3a b) + 5
c)
2a2 + 3 (a + 2b)(2a b) + 5b2
d)
7b2 + 5 (a + b)(a + 2b) (3a + b)(2a 2b) + 7(a + 1)

a)
a2 + 4(3a + b)(7a + 2b) + 3b2 (2 + 5b)
b)
ab + 3b 4 + 2(6a 3b) 4ab + (a + 2b)(3a b) + 5
c)
2a2 + 3 (a + 2b)(2a b) + 5b2
d)
7b2 + 5 (a + b)(a + 2b) (3a + b)(2a 2b) + 7(a + 1)

1.14)

Contract the expressions:

a)
a + 4b 2 + 3a 7b 3
b)
3x 5y 3 + 8y + 4x 4
c)
6y + 9x 5 2x 3y 6
d)
12b + 4a 8 + 7a 5b 5
e)
14b 7a 9 4b 3a 3
f)
20m + 12n 14 + 6n 8m 5
g)
2(4p + 3a) 8 3(p 4a) 6
h)
5k + 5h 4 + 17k + 22h 12

a)
a + 4b 2 + 3a 7b 3
b)
3x 5y 3 + 8y + 4x 4
c)
6y + 9x 5 2x 3y 6
d)
12b + 4a 8 + 7a 5b 5
e)
14b 7a 9 4b 3a 3
f)
20m + 12n 14 + 6n 8m 5
g)
2(4p + 3a) 8 3(p 4a) 6
h)
5k + 5h 4 + 17k + 22h 12

1.15)

Contract the expressions:

a)
2(4x + 3) a + 3(7 2x) b
b)
5(x 2) 3a (5x + 3) 3b
c)
9p + 3d c + 6(7p 4) 5c
d)
4(12x + 3z) x 10(z + 3) 4
e)
2x(3a 6b) t + a(4x b) r
f)
3p(2 + p) p2 3(2p p) p
g)
(4 x)(x + 3) 4x + (0 3x)5 8
h)
(3a + 4b)(5b 2a) 6x + (8a + 2b)(3a 4b) 4x

1.16)

Expand the expressions:

a)
(4x 3b) 5a (b + 7x) 3c
b)
(2a + 5b) 12d (8a + 3b) 3k
c)
(6b 3a) 4c (9a 5b) 7c
d)
(8a + 2b) 7n (4a 6b) 3n
e)
2(2a + 2b) (a + b) (2a + 2b) (a b)
f)
4(g + 5h) (3a 5b) 9(2h + 3g) (2b 3a)
g)
(15n + 12m) (6b 4a) (2n m) (2a + 3b)
h)
9p (a b) (4s 6r)3 (a b)

a)
(4x 3b) 5a (b + 7x) 3c
b)
(2a + 5b) 12d (8a + 3b) 3k
c)
(6b 3a) 4c (9a 5b) 7c
d)
(8a + 2b) 7n (4a 6b) 3n
e)
2(2a + 2b) (a + b) (2a + 2b) (a b)
f)
4(g + 5h) (3a 5b) 9(2h + 3g) (2b 3a)
g)
(15n + 12m) (6b 4a) (2n m) (2a + 3b)
h)
9p (a b) (4s 6r)3 (a b)

You can find the solutions here.

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