Free Printable 4. Using the Distributive Law

1.

What does the Distributive Law mean?

a)

states that for any numbers a, b, and c, the equation a(b + c) = ab + ac is true.

b)

states that for any numbers a, b, and c, the equation a(b + c) = ab x ac is true.

c)

states that for any numbers a, b, and c, the equation a(b + c) = a + b + a + c is true.

d)

states that for any numbers a, b, and c, the equation a(b + c) = a - b + ac is true.

2.

Rewrite using the Distributive Law: 6(3 + 6)

a)

(6x3) + 6

b)

63

c)

(6x3) + (6x6)

d)

18 + 36

3.

Which of the following expressions represents the total area of the rectangle? (Remember: A = L x W)

a)

5(2 + 3)

b)

3(2 + 5)

c)

2(3 + 5)

d)

2(3) + 3(5)

4.

Match the definition with the term: The largest factor that two or more numbers or terms have in common.

a)

Like Term

b)

Highest Common Factor

c)

Common Factor

d)

Term

5.

The Highest Common Factor (HCF) of 8 and 12

a)

24

b)

4

c)

20

d)

2

e)

3

6.

Factorise: $5x+5$

a)

$5(x+1)$

b)

$5(x+5)$

c)

$10x$

d)

$5(5x+1)$

7.

Factorise: $3x+12$

a)

$3(x+12)$

b)

$15$

c)

$3(x+4)$

d)

$3(x+9)$

8.

Factor: $6x+9$

a)

$2(x+3)$

b)

$3(x+3)$

c)

$6(x+3)$

d)

$3(2x+3)$

9.

Factor the expression by the GCF.

12x-20

(a)

10.

Factor the expression using the HCF.

15x + 25

a)

5(3x + 5)

b)

10(5x + 15)

c)

3(5x + 8)

d)

15(x + 10)

11.

Factor in simplest form (using HCF): 6x + 12

a)

3(2x + 4)

b)

6(x+2)

c)

6x(x+2)

d)

1/2 (3x + 24)

12.

Which of the expressions is equivalent to 7x - 14?

a)

7(x - 2)

b)

7(x + 2)

c)

7x + 14

d)

7(x - 14)

13.

Which of the following expressions is equivalent to 10x + 8?

a)

10x - 8

b)

5x + 5x + 4

c)

5(5x + 3)

d)

2(5x + 4)

14.

Factor the terms:

24c-18

a)

$6\left(4c+3\right)$

b)

$6\left(4c-3\right)$

c)

$2\left(12c-9\right)$

d)

$2\left(-12c+9\right)$

15.

Factor in simplest form:

p² - 14p

a)

14(p² - p)

b)

2p(p - 7)

c)

p²(1 - 14)

d)

p(p - 14)

4. Using the Distributive Law - Factorising

Total questions: 15

Worksheet time: 12mins

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