Multiply Binomials

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Question 1 of 6

1. Question
Expand and simplify.

`(x+2)(x-5)`
- `x^2-3x-10`
- `x^2-5x+3`
- `x^2-4x-5`
- `x^2+x-6`
Hint

Help Video

Correct

Correct!

Incorrect

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

Step `1`: Write out one binomial twice.

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

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

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

Step `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^2-5x+2x-10`

Step `4`: Collect like terms and simplify.

`x^2` `-5x+2x` `-10`

`=` `x^2-3x-10`

`x^2-3x-10`
Question 2 of 6

2. Question
Expand and simplify.

`(x-8)(x+3)`
- `x^2-5x-24`
- `x^2-8x+4`
- `x^2+2x-16`
- `x^2-7x-4`
Hint

Help Video

Correct

Great Work!

Incorrect

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

Step `1`: Write out one binomial twice.

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

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

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

Step `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+3x-8x-24`

Step `4`: Collect like terms and simplify.

`x^2` `+3x-8x` `-24`

`=` `x^2-5x-24`

`x^2-5x-24`
Question 3 of 6

3. Question
Expand and simplify.

`(x+7)(x-4)`
- `x^2+3x-28`
- `x^2-4x-32`
- `2x^2+4x-22`
- `x^2+4x+16`
Hint

Help Video

Correct

Keep Going!

Incorrect

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

Step `1`: Write out one binomial twice.

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

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

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

Step `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^2-4x+7x-28`

Step `4`: Collect like terms and simplify.

`x^2` `-4x+7x` `-28`

`=` `x^2+3x-28`

`x^2+3x-28`

Question 4 of 6

4. Question

Expand and simplify.

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

`6x^2-9x-20`
`3x^2-6x-15`
`6x^2-21x-9`
`4x^2-8x+18`

Hint

Help Video

Correct

Fantastic!

Incorrect

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

Step `1`: Write out one binomial twice.

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

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

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

Step `3`: Expand by multiplying each binomial.

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

Step `4`: Collect like terms and simplify.

		`6x^2` `-15x+6x` `-20`
	`=`	`6x^2-9x-20`

`6x^2-9x-20`

Question 5 of 6

5. Question

Expand and simplify.

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

`15m^2-7m-4`
`10m^2+17m-8`
`20m^2-7m+20`
`15m^2+21m-10`

Hint

Help Video

Correct

Excellent!

Incorrect

Distributive Property

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

6. Question

Expand and simplify.

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

`16a^2+22a-3`
`8a^2+11a-6`
`16a^2-26a+4`
`14a^2+18a-6`

Hint

Help Video

Correct

Well Done!

Incorrect

Distributive Property

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`

Quizzes

Multiply Binomials
Multiply Binomials – FOIL Method
FOIL Method – Same First Variable 1
FOIL Method – Same First Variable 2
FOIL Method – 3 Terms
Expand Perfect Squares
Difference of Two Squares
Difference of Two Squares (Longer Expressions)

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

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

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

		`x^2` `-5x+2x` `-10`
	`=`	`x^2-3x-10`

		`x^2` `+3x-8x` `-24`
	`=`	`x^2-5x-24`

		`x^2` `-4x+7x` `-28`
	`=`	`x^2+3x-28`

Multiply Binomials

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Quiz summary

Information

1. Question

Hint

Correct!

Distributive Property

2. Question

Hint

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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