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Factor Difference of Two Squares 3Factor Difference of Two Squares 3
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Question 1 of 4
1. Question
Factor.`1/4y^225x^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.`1/4y^225x^2` `=` `(1/2y)^225x^2` `(1/2y)^2=1/4y^2` `=` `(1/2y)^2(5x)^2` `(5x)^2=25x^2` Next, label the values in the expression.$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$`(1/2y)^2(5x)^2``a=1/2y``b=5x`Substitute the values into the formula given for Factoring the Difference of Two Squares.$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}\color{#9a00c7}{b})$$ $$\left(\color{#00880A}{\frac{1}{2}y}\right)^2(\color{#9a00c7}{5x})^2$$ `=` $$\left(\color{#00880A}{\frac{1}{2}y}+\color{#9a00c7}{5x}\right)\left(\color{#00880A}{\frac{1}{2}y}\color{#9a00c7}{5x}\right)$$ `(1/2y+5x)(1/2y5x)` 
Question 2 of 4
2. Question
Factor.`9n^21/9`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.`9n^21/9` `=` `(3n)^21/9` `(3n)^2=9n^2` `=` `(3n)^2(1/3)^2` `(1/3)^2=1/9` Next, label the values in the expression.$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$`(3n)^2(1/3)^2``a=3n``b=1/3`Substitute the values into the formula given for Factoring the Difference of Two Squares.$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}\color{#9a00c7}{b})$$ $$(\color{#00880A}{3n})^2\left(\color{#9a00c7}{\frac{1}{3}}\right)^2$$ `=` $$\left(\color{#00880A}{3n}+\color{#9a00c7}{\frac{1}{3}}\right)\left(\color{#00880A}{3n}\color{#9a00c7}{\frac{1}{3}}\right)$$ `(3n+1/3)(3n1/3)` 
Question 3 of 4
3. Question
Factor.`(x^2)/(16)(y^2)/(36)`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^2)/(16)(y^2)/(36)` `=` `(x/4)^2(y^2)/(36)` `(x/4)^2=(x^2)/(16)` `=` `(x/4)^2(y/6)^2` `(y/6)^2=(y^2)/(36)` Next, label the values in the expression.$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$`(x/4)^2(y/6)^2``a=x/4``b=y/6`Substitute the values into the formula given for Factoring the Difference of Two Squares.$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}\color{#9a00c7}{b})$$ $$\left(\color{#00880A}{\frac{x}{4}}\right)^2\left(\color{#9a00c7}{\frac{y}{6}}\right)^2$$ `=` $$\left(\color{#00880A}{\frac{x}{4}}+\color{#9a00c7}{\frac{y}{6}}\right)\left(\color{#00880A}{\frac{x}{4}}\color{#9a00c7}{\frac{y}{6}}\right)$$ `(x/4+y/6)(x/4y/6)` 
Question 4 of 4
4. Question
Factor.`64x^22 1/4`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.`64x^22 1/4` `=` `(8x)^22 1/4` `(8x)^2=64x^2` `=` `(8x)^29/4` Convert the second term to an improper fraction `=` `(8x)^2(3/2)^2` `(3/2)^2=9/4` Next, label the values in the expression.$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$`(8x)^2(3/2)^2``a=8x``b=3/2`Substitute the values into the formula given for Factoring the Difference of Two Squares.$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}\color{#9a00c7}{b})$$ $$(\color{#00880A}{8x})^2\left(\color{#9a00c7}{\frac{3}{2}}\right)^2$$ `=` $$\left(\color{#00880A}{8x}+\color{#9a00c7}{\frac{3}{2}}\right)\left(\color{#00880A}{8x}\color{#9a00c7}{\frac{3}{2}}\right)$$ `(8x+3/2)(8x3/2)`
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