Multiply Binomials

Question 1 of 6

Expand and simplify.

(x + 2) (x - 5)

$(x+2)(x-5)$

1. $x^{2} - 5 x + 3$ $x^2-5x+3$
2. $x^{2} + x - 6$ $x^2+x-6$
3. $x^{2} - 3 x - 10$ $x^2-3x-10$
4. $x^{2} - 4 x - 5$ $x^2-4x-5$

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Distributive Property

(a + b) (c + d) = a (c + d) + b (c + d) = a c + a d + b c + b d

$(\color{#00880A}{a}+\color{#00880A}{b})(\color{#9a00c7}{c}+\color{#9a00c7}{d})=\color{#00880A}{a}(\color{#9a00c7}{c}+\color{#9a00c7}{d})+\color{#00880A}{b}(\color{#9a00c7}{c}+\color{#9a00c7}{d})=\color{#00880A}{a}\color{#9a00c7}{c}+\color{#00880A}{a}\color{#9a00c7}{d}+\color{#00880A}{b}\color{#9a00c7}{c}+\color{#00880A}{b}\color{#9a00c7}{d}$

Use the Distributive Property to expand the expression: $(\color{#00880A}{x}+\color{#00880A}{2})(\color{#9a00c7}{x}-\color{#9a00c7}{5})$

Step $1$ $1$ : Write out one binomial twice.

(x - 5) (x - 5)

$\;\;\;\;\;\;(\color{#9a00c7}{x}-\color{#9a00c7}{5})\;\;\;\;\;\;(\color{#9a00c7}{x}-\color{#9a00c7}{5})$

Step $2$ $2$ : Split and distribute the other binomial.

x (x - 5) + 2 (x - 5)

$\;\;\;\;\color{#00880A}{x}(\color{#9a00c7}{x}-\color{#9a00c7}{5})+\color{#00880A}{2}(\color{#9a00c7}{x}-\color{#9a00c7}{5})$

Step $3$ $3$ : Expand by multiplying each binomial.

		$(\color{#00880A}{x})(\color{#9a00c7}{x})-(\color{#00880A}{x})(\color{#9a00c7}{5})+(\color{#00880A}{2})(\color{#9a00c7}{x})-(\color{#00880A}{2})(\color{#9a00c7}{5})$
	$=$ $=$	$x^{2} - 5 x + 2 x - 10$ $x^2-5x+2x-10$

Step $4$ $4$ : Collect like terms and simplify.

		$x^{2}$ $x^2$ $- 5 x + 2 x$ $-5x+2x$ $- 10$ $-10$
	$=$ $=$	$x^{2} - 3 x - 10$ $x^2-3x-10$

x^{2} - 3 x - 10

$x^2-3x-10$

Question 2 of 6

Expand and simplify.

(x - 8) (x + 3)

$(x-8)(x+3)$

1. $x^{2} + 2 x - 16$ $x^2+2x-16$
2. $x^{2} - 7 x - 4$ $x^2-7x-4$
3. $x^{2} - 8 x + 4$ $x^2-8x+4$
4. $x^{2} - 5 x - 24$ $x^2-5x-24$

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Distributive Property

(a + b) (c + d) = a (c + d) + b (c + d) = a c + a d + b c + b d

$(\color{#00880A}{a}+\color{#00880A}{b})(\color{#9a00c7}{c}+\color{#9a00c7}{d})=\color{#00880A}{a}(\color{#9a00c7}{c}+\color{#9a00c7}{d})+\color{#00880A}{b}(\color{#9a00c7}{c}+\color{#9a00c7}{d})=\color{#00880A}{a}\color{#9a00c7}{c}+\color{#00880A}{a}\color{#9a00c7}{d}+\color{#00880A}{b}\color{#9a00c7}{c}+\color{#00880A}{b}\color{#9a00c7}{d}$

Use the Distributive Property to expand the expression: $(\color{#00880A}{x}-\color{#00880A}{8})(\color{#9a00c7}{x}+\color{#9a00c7}{3})$

Step $1$ $1$ : Write out one binomial twice.

(x + 3) (x + 3)

$\;\;\;\;\;\;(\color{#9a00c7}{x}+\color{#9a00c7}{3})\;\;\;\;\;\;(\color{#9a00c7}{x}+\color{#9a00c7}{3})$

Step $2$ $2$ : Split and distribute the other binomial.

x (x + 3) - 8 (x + 3)

$\;\;\;\;\color{#00880A}{x}(\color{#9a00c7}{x}+\color{#9a00c7}{3})-\color{#00880A}{8}(\color{#9a00c7}{x}+\color{#9a00c7}{3})$

Step $3$ $3$ : Expand by multiplying each binomial.

		$(\color{#00880A}{x})(\color{#9a00c7}{x})+(\color{#00880A}{x})(\color{#9a00c7}{3})-(\color{#00880A}{8})(\color{#9a00c7}{x})-(\color{#00880A}{8})(\color{#9a00c7}{3})$
	$=$ $=$	$x^{2} + 3 x - 8 x - 24$ $x^2+3x-8x-24$

Step $4$ $4$ : Collect like terms and simplify.

		$x^{2}$ $x^2$ $+ 3 x - 8 x$ $+3x-8x$ $- 24$ $-24$
	$=$ $=$	$x^{2} - 5 x - 24$ $x^2-5x-24$

x^{2} - 5 x - 24

$x^2-5x-24$

Question 3 of 6

Expand and simplify.

(x + 7) (x - 4)

$(x+7)(x-4)$

1. $x^{2} + 3 x - 28$ $x^2+3x-28$
2. $2 x^{2} + 4 x - 22$ $2x^2+4x-22$
3. $x^{2} - 4 x - 32$ $x^2-4x-32$
4. $x^{2} + 4 x + 16$ $x^2+4x+16$

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Distributive Property

(a + b) (c + d) = a (c + d) + b (c + d) = a c + a d + b c + b d

$(\color{#00880A}{a}+\color{#00880A}{b})(\color{#9a00c7}{c}+\color{#9a00c7}{d})=\color{#00880A}{a}(\color{#9a00c7}{c}+\color{#9a00c7}{d})+\color{#00880A}{b}(\color{#9a00c7}{c}+\color{#9a00c7}{d})=\color{#00880A}{a}\color{#9a00c7}{c}+\color{#00880A}{a}\color{#9a00c7}{d}+\color{#00880A}{b}\color{#9a00c7}{c}+\color{#00880A}{b}\color{#9a00c7}{d}$

Use the Distributive Property to expand the expression: $(\color{#00880A}{x}+\color{#00880A}{7})(\color{#9a00c7}{x}-\color{#9a00c7}{4})$

Step $1$ $1$ : Write out one binomial twice.

(x - 4) (x - 4)

$\;\;\;\;\;\;(\color{#9a00c7}{x}-\color{#9a00c7}{4})\;\;\;\;\;\;(\color{#9a00c7}{x}-\color{#9a00c7}{4})$

Step $2$ $2$ : Split and distribute the other binomial.

x (x - 4) + 7 (x - 4)

$\;\;\;\;\color{#00880A}{x}(\color{#9a00c7}{x}-\color{#9a00c7}{4})+\color{#00880A}{7}(\color{#9a00c7}{x}-\color{#9a00c7}{4})$

Step $3$ $3$ : Expand by multiplying each binomial.

		$(\color{#00880A}{x})(\color{#9a00c7}{x})-(\color{#00880A}{x})(\color{#9a00c7}{4})+(\color{#00880A}{7})(\color{#9a00c7}{x})-(\color{#00880A}{7})(\color{#9a00c7}{4})$
	$=$ $=$	$x^{2} - 4 x + 7 x - 28$ $x^2-4x+7x-28$

Step $4$ $4$ : Collect like terms and simplify.

		$x^{2}$ $x^2$ $- 4 x + 7 x$ $-4x+7x$ $- 28$ $-28$
	$=$ $=$	$x^{2} + 3 x - 28$ $x^2+3x-28$

x^{2} + 3 x - 28

$x^2+3x-28$

Question 4 of 6

Expand and simplify.

(3 x + 4) (2 x - 5)

$(3x+4)(2x-5)$

1. $6 x^{2} - 21 x - 9$ $6x^2-21x-9$
2. $6 x^{2} - 9 x - 20$ $6x^2-9x-20$
3. $3 x^{2} - 6 x - 15$ $3x^2-6x-15$
4. $4 x^{2} - 8 x + 18$ $4x^2-8x+18$

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Distributive Property

(a + b) (c + d) = a (c + d) + b (c + d) = a c + a d + b c + b d

$(\color{#00880A}{a}+\color{#00880A}{b})(\color{#9a00c7}{c}+\color{#9a00c7}{d})=\color{#00880A}{a}(\color{#9a00c7}{c}+\color{#9a00c7}{d})+\color{#00880A}{b}(\color{#9a00c7}{c}+\color{#9a00c7}{d})=\color{#00880A}{a}\color{#9a00c7}{c}+\color{#00880A}{a}\color{#9a00c7}{d}+\color{#00880A}{b}\color{#9a00c7}{c}+\color{#00880A}{b}\color{#9a00c7}{d}$

Use the Distributive Property to expand the expression: $(\color{#00880A}{3x}+\color{#00880A}{4})(\color{#9a00c7}{2x}-\color{#9a00c7}{5})$

Step $1$ $1$ : Write out one binomial twice.

(2 x - 5) (2 x - 5)

$\;\;\;\;\;\;(\color{#9a00c7}{2x}-\color{#9a00c7}{5})\;\;\;\;\;\;(\color{#9a00c7}{2x}-\color{#9a00c7}{5})$

Step $2$ $2$ : Split and distribute the other binomial.

3 x (2 x - 5) + 4 (2 x - 5)

$\;\;\;\;\color{#00880A}{3x}(\color{#9a00c7}{2x}-\color{#9a00c7}{5})+\color{#00880A}{4}(\color{#9a00c7}{2x}-\color{#9a00c7}{5})$

Step $3$ $3$ : Expand by multiplying each binomial.

		$(\color{#00880A}{3x})(\color{#9a00c7}{2x})-(\color{#00880A}{3x})(\color{#9a00c7}{5})+(\color{#00880A}{4})(\color{#9a00c7}{2x})-(\color{#00880A}{4})(\color{#9a00c7}{5})$
	$=$ $=$	$6 x^{2} - 15 x + 6 x - 20$ $6x^2-15x+6x-20$

Step $4$ $4$ : Collect like terms and simplify.

		$6 x^{2}$ $6x^2$ $- 15 x + 6 x$ $-15x+6x$ $- 20$ $-20$
	$=$ $=$	$6 x^{2} - 9 x - 20$ $6x^2-9x-20$

6 x^{2} - 9 x - 20

$6x^2-9x-20$

Question 5 of 6

Expand and simplify.

(5 m - 4) (3 m + 1)

$(5m-4)(3m+1)$

1. $15m^2-7m-4$
2. $15m^2+21m-10$
3. $10m^2+17m-8$
4. $20m^2-7m+20$

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Distributive Property

$(\color{#00880A}{a}+\color{#00880A}{b})(\color{#9a00c7}{c}+\color{#9a00c7}{d})=\color{#00880A}{a}(\color{#9a00c7}{c}+\color{#9a00c7}{d})+\color{#00880A}{b}(\color{#9a00c7}{c}+\color{#9a00c7}{d})=\color{#00880A}{a}\color{#9a00c7}{c}+\color{#00880A}{a}\color{#9a00c7}{d}+\color{#00880A}{b}\color{#9a00c7}{c}+\color{#00880A}{b}\color{#9a00c7}{d}$

Use the Distributive Property to expand the expression: $(\color{#00880A}{5m}-\color{#00880A}{4})(\color{#9a00c7}{3m}+\color{#9a00c7}{1})$

Step $1$ : Write out one binomial twice.

$\;\;\;\;\;\;(\color{#9a00c7}{3m}+\color{#9a00c7}{1})\;\;\;\;\;\;(\color{#9a00c7}{3m}+\color{#9a00c7}{1})$

Step $2$ : Split and distribute the other binomial.

$\;\;\;\;\color{#00880A}{5m}(\color{#9a00c7}{3m}+\color{#9a00c7}{1})-\color{#00880A}{4}(\color{#9a00c7}{3m}+\color{#9a00c7}{1})$

Step $3$ : Expand by multiplying each binomial.

		$(\color{#00880A}{5m})(\color{#9a00c7}{3m})+(\color{#00880A}{5m})(\color{#9a00c7}{1})-(\color{#00880A}{4})(\color{#9a00c7}{3m})-(\color{#00880A}{4})(\color{#9a00c7}{1})$
	$=$	$15m^2+5m-12m-4$

Step $4$ : Collect like terms and simplify.

		$15m^2$ $+5m-12m$ $-4$
	$=$	$15m^2-7m-4$

$15m^2-7m-4$

Question 6 of 6

Expand and simplify.

$(8a-1)(2a+3)$

1. $16a^2-26a+4$
2. $16a^2+22a-3$
3. $8a^2+11a-6$
4. $14a^2+18a-6$

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Distributive Property

$(\color{#00880A}{a}+\color{#00880A}{b})(\color{#9a00c7}{c}+\color{#9a00c7}{d})=\color{#00880A}{a}(\color{#9a00c7}{c}+\color{#9a00c7}{d})+\color{#00880A}{b}(\color{#9a00c7}{c}+\color{#9a00c7}{d})=\color{#00880A}{a}\color{#9a00c7}{c}+\color{#00880A}{a}\color{#9a00c7}{d}+\color{#00880A}{b}\color{#9a00c7}{c}+\color{#00880A}{b}\color{#9a00c7}{d}$

Use the Distributive Property to expand the expression: $(\color{#00880A}{8a}-\color{#00880A}{1})(\color{#9a00c7}{2a}+\color{#9a00c7}{3})$

Step $1$ : Write out one binomial twice.

$\;\;\;\;\;\;(\color{#9a00c7}{2a}+\color{#9a00c7}{3})\;\;\;\;\;\;(\color{#9a00c7}{2a}+\color{#9a00c7}{3})$

Step $2$ : Split and distribute the other binomial.

$\;\;\;\;\color{#00880A}{8a}(\color{#9a00c7}{2a}+\color{#9a00c7}{3})-\color{#00880A}{1}(\color{#9a00c7}{2a}+\color{#9a00c7}{3})$

Step $3$ : Expand by multiplying each binomial.

		$(\color{#00880A}{8a})(\color{#9a00c7}{2a})+(\color{#00880A}{8a})(\color{#9a00c7}{3})-(\color{#00880A}{1})(\color{#9a00c7}{2a})-(\color{#00880A}{1})(\color{#9a00c7}{3})$
	$=$	$16a^2+24a-2a-3$

Step $4$ : Collect like terms and simplify.

		$16a^2$ $+24a-2a$ $-3$
	$=$	$16a^2+22a-3$

$16a^2+22a-3$

Multiply Binomials

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Quiz summary

Information

1. Question

Hint

Correct!

Distributive Property

2. Question

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Great Work!

Distributive Property

3. Question

Hint

Keep Going!

Distributive Property

4. Question

Hint

Fantastic!

Distributive Property

5. Question

Hint

Excellent!

Distributive Property

6. Question

Hint

Well Done!

Distributive Property

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