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Factor Difference of Two Squares>
Factor Difference of Two Squares 2Factor Difference of Two Squares 2
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Question 1 of 4
1. Question
Factor.`36m^2-121n^2`Hint
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Exceptional!
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Factoring the Difference of Two Squares
$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2=(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$$First, express both terms of the polynomial as perfect squares. In other words, both terms should have `2` as their exponent.`36m^2-121n^2` `=` `(6m)^2-121n^2` `(6m)^2=36m^2` `=` `(6m)^2-(11n)^2` `(11n)^2=121n^2` Next, label the values in the expression.$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$`(6m)^2-(11n)^2``a=6m``b=11n`Substitute the values into the formula given for Factoring the Difference of Two Squares.$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$$ $$(\color{#00880A}{6m})^2-(\color{#9a00c7}{11n})^2$$ `=` $$(\color{#00880A}{6m}+\color{#9a00c7}{11n})(\color{#00880A}{6m}-\color{#9a00c7}{11n})$$ `(6m+11n)(6m-11n)` -
Question 2 of 4
2. Question
Factor.`x^2y^2-z^2`Hint
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Factoring the Difference of Two Squares
$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2=(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$$First, express both terms of the polynomial as perfect squares. In other words, both terms should have `2` as their exponent.`x^2y^2-z^2` `=` `(xy)^2-z^2` `(xy)^2=x^2y^2` Next, label the values in the expression.$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$`(xy)^2-z^2``a=xy``b=z`Substitute the values into the formula given for Factoring the Difference of Two Squares.$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$$ $$(\color{#00880A}{xy})^2-\color{#9a00c7}{z}^2$$ `=` $$(\color{#00880A}{xy}+\color{#9a00c7}{z})(\color{#00880A}{xy}-\color{#9a00c7}{z})$$ `(xy+z)(xy-z)` -
Question 3 of 4
3. Question
Factor.`4a^2-9b^2c^2`Hint
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Nice Job!
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Factoring the Difference of Two Squares
$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2=(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$$First, express both terms of the polynomial as perfect squares. In other words, both terms should have `2` as their exponent.`4a^2-9b^2c^2` `=` `(2a)^2-9b^2c^2` `(2a)^2=4a^2` `=` `(4a)^2-(3bc)^2` `(3bc)^2=9b^2c^2` Next, label the values in the expression.$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$`(2a)^2-(3bc)^2``a=2a``b=3bc`Substitute the values into the formula given for Factoring the Difference of Two Squares.$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$$ $$(\color{#00880A}{2a})^2-(\color{#9a00c7}{3bc})^2$$ `=` $$(\color{#00880A}{2a}+\color{#9a00c7}{3bc})(\color{#00880A}{2a}-\color{#9a00c7}{3bc})$$ `(2a+3bc)(2a-3bc)` -
Question 4 of 4
4. Question
Factor.`16a^2b^2-81c^2d^2`Hint
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Excellent!
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Factoring the Difference of Two Squares
$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2=(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$$First, express both terms of the polynomial as perfect squares. In other words, both terms should have `2` as their exponent.`16a^2b^2-81c^2d^2` `=` `(4ab)^2-81c^2d^2` `(4ab)^2=16a^2b^2` `=` `(4ab)^2-(9cd)^2` `(9cd)^2=81c^2d^2` Next, label the values in the expression.$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$`(4ab)^2-(9cd)^2``a=4ab``b=9cd`Substitute the values into the formula given for Factoring the Difference of Two Squares.$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$$ $$(\color{#00880A}{4ab})^2-(\color{#9a00c7}{9cd})^2$$ `=` $$(\color{#00880A}{4ab}+\color{#9a00c7}{9cd})(\color{#00880A}{4ab}-\color{#9a00c7}{9cd})$$ `(4ab+9cd)(4ab-9cd)`
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