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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^2-25x^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^2-25x^2` `=` `(1/2y)^2-25x^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)(1/2y-5x)` -
Question 2 of 4
2. Question
Factor.`9n^2-1/9`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^2-1/9` `=` `(3n)^2-1/9` `(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)(3n-1/3)` -
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/4-y/6)` -
Question 4 of 4
4. Question
Factor.`64x^2-2 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^2-2 1/4` `=` `(8x)^2-2 1/4` `(8x)^2=64x^2` `=` `(8x)^2-9/4` 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)(8x-3/2)`
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