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Binomial Products – Distributive PropertyBinomial Products – Distributive Property
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Question 1 of 6
1. Question
Expand and simplify.`(x+2)(x-5)`Hint
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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)`Hint
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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)`Hint
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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)`Hint
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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)`Hint
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Excellent!
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: $$(\color{#00880A}{5m}-\color{#00880A}{4})(\color{#9a00c7}{3m}+\color{#9a00c7}{1})$$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)`Hint
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Well Done!
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: $$(\color{#00880A}{8a}-\color{#00880A}{1})(\color{#9a00c7}{2a}+\color{#9a00c7}{3})$$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`