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Factor Difference of Two Squares>
Factor Difference of Two Squares 1Factor Difference of Two Squares 1
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Question 1 of 5
1. Question
Factor.`x^2-25`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^2-25` `=` `x^2-5^2` `5^2=25` Next, label the values in the expression.$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$`x^2-5^2``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)(x-5)` -
Question 2 of 5
2. Question
Factor.`b^2-121`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^2-121` `=` `b^2-11^2` `11^2=121` Next, label the values in the expression.$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$`b^2-11^2``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)(b-11)` -
Question 3 of 5
3. Question
Factor.`144-v^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.`144-v^2` `=` `12^2-v^2` `12^2=144` Next, label the values in the expression.$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$`12^2-v^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)(12-v)` -
Question 4 of 5
4. Question
Factor.`4x^2-9`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.`4x^2-9` `=` `(2x)^2-9` `(2x)^2=4x^2` `=` `(2x)^2-3^2` `3^2=9` Next, label the values in the expression.$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$`(2x)^2-3^2``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)(2x-3)` -
Question 5 of 5
5. Question
Factor.`16a^2-1`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^2-1` `=` `(4a)^2-1` `(4a)^2=16a^2` `=` `(4a)^2-1^2` `1^2=1` Next, label the values in the expression.$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$`(4a)^2-1^2``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)(4a-1)`
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