Colorful House of Math logo
Log in

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.

Want to know more?Sign UpIt's free!
White arrow pointing to the LeftPrevious entry
Combining the Rules
Next entryWhite arrow pointing to the right
The First and Second Algebraic Identity