Binomial Products – Distributive Property

Years

Try VividMath Premium to unlock full access

Start Free Trial

Time limit: 0

Quiz summary

0 of 6 questions completed

Questions:

Information

–

You have already completed the quiz before. Hence you can not start it again.

Quiz is loading...

You must sign in or sign up to start the quiz.

You have to finish following quiz, to start this quiz:

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

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

Binomial Products – Distributive Property
Binomial Products – 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
Expand Longer Expressions
Highest Common Factor 1
Highest Common Factor 2
Factorise a Polynomial (HCF)
Factorise a Polynomial 1
Factorise a Polynomial 2
Factorise a Polynomial with Integers
Factorise Difference of Two Squares 1
Factorise Difference of Two Squares 2
Factorise Difference of Two Squares 3
Factorise by Grouping in Pairs
Factorise Difference of Two Squares (Harder) 1
Factorise Difference of Two Squares (Harder) 2
Factorise Difference of Two Squares (Harder) 3
Factorise Trinomials (Quadratics) 1
Factorise Trinomials (Quadratics) 2
Factorise Trinomials (Quadratics) 3
Factorise Trinomials (Quadratics) w Coefficient more than 1 (1)
Factorise Trinomials (Quadratics) w Coefficient more than 1 (2)
Factorise Trinomials (Quadratics) w Coefficient more than 1 (3)
Factorise Trinomials (Quadratics) – Complex

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

Binomial Products – Distributive Property

Try VividMath Premium to unlock full access

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

Quizzes