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Factor Difference of Two Squares 1Factor Difference of Two Squares 1
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Question 1 of 5
1. Question
Factor.`x^225`Hint
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Factor 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^225` `=` `x^25^2` `5^2=25` Next, label the values in the expression.$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$`x^25^2``a=x``b=5`Substitute the values into the formula given for Factoring the Difference of Two Squares.$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}\color{#9a00c7}{b})$$ $$\color{#00880A}{x}^2\color{#9a00c7}{5}^2$$ `=` $$(\color{#00880A}{x}+\color{#9a00c7}{5})(\color{#00880A}{x}\color{#9a00c7}{5})$$ `(x+5)(x5)` 
Question 2 of 5
2. Question
Factor.`b^2121`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.`b^2121` `=` `b^211^2` `11^2=121` Next, label the values in the expression.$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$`b^211^2``a=b``b=11`Substitute the values into the formula given for Factoring the Difference of Two Squares.$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}\color{#9a00c7}{b})$$ $$\color{#00880A}{b}^2\color{#9a00c7}{11}^2$$ `=` $$(\color{#00880A}{b}+\color{#9a00c7}{11})(\color{#00880A}{b}\color{#9a00c7}{11})$$ `(b+11)(b11)` 
Question 3 of 5
3. Question
Factor.`144v^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.`144v^2` `=` `12^2v^2` `12^2=144` Next, label the values in the expression.$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$`12^2v^2``a=12``b=v`Substitute the values into the formula given for Factoring the Difference of Two Squares.$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}\color{#9a00c7}{b})$$ $$\color{#00880A}{12}^2\color{#9a00c7}{v}^2$$ `=` $$(\color{#00880A}{12}+\color{#9a00c7}{v})(\color{#00880A}{12}\color{#9a00c7}{v})$$ `(12+v)(12v)` 
Question 4 of 5
4. Question
Factor.`4x^29`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.`4x^29` `=` `(2x)^29` `(2x)^2=4x^2` `=` `(2x)^23^2` `3^2=9` Next, label the values in the expression.$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$`(2x)^23^2``a=2x``b=3`Substitute the values into the formula given for Factoring the Difference of Two Squares.$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}\color{#9a00c7}{b})$$ $$(\color{#00880A}{2x})^2\color{#9a00c7}{3}^2$$ `=` $$(\color{#00880A}{2x}+\color{#9a00c7}{3})(\color{#00880A}{2x}\color{#9a00c7}{3})$$ `(2x+3)(2x3)` 
Question 5 of 5
5. Question
Factor.`16a^21`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.`16a^21` `=` `(4a)^21` `(4a)^2=16a^2` `=` `(4a)^21^2` `1^2=1` Next, label the values in the expression.$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$`(4a)^21^2``a=4a``b=1`Substitute the values into the formula given for Factoring the Difference of Two Squares.$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}\color{#9a00c7}{b})$$ $$(\color{#00880A}{4a})^2\color{#9a00c7}{1}^2$$ `=` $$(\color{#00880A}{4a}+\color{#9a00c7}{1})(\color{#00880A}{4a}\color{#9a00c7}{1})$$ `(4a+1)(4a1)`
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