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Factor Difference of Two Squares (Harder)>
Factor Difference of Two Squares (Harder) 2Factor Difference of Two Squares (Harder) 2
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Question 1 of 4
1. Question
Factor.`2x^5128x^3`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, find the Greatest Common Factor (GCF) of the two terms.Start by listing down their factors.Factors of `2x^5`: `2``times``x``times``x``times``x``timesxtimesx`Factors of `128x^3`: `2``times64times``x``times``x``times``x`Collect the common factors and multiply them all to get the GCF.GCF `=` `2``times``x``times``x``times``x` `=` `2x^3` Next, factor by placing `2x^3` outside a bracket.Also, place the given polynomial inside the bracket with each term divided by `2x^3`, then simplify.`2x^3[(2x^5div2x^3)(128x^3div2x^3)]` `=` `2x^3(x^264)` Now, express both terms inside the parenthesis as perfect squares. In other words, both terms should have `2` as their exponent.`x^264` `=` `x^28^2` `8^2=64` Finally, label the values in the expression `x^28^2` and substitute the values into the formula given for Factoring the Difference of Two Squares.`a=x``b=8`$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$$ $$2x^3(\color{#00880A}{x}^2\color{#9a00c7}{8}^2)$$ `=` $$2x^3(\color{#00880A}{x}\color{#9a00c7}{8})(\color{#00880A}{x}+\color{#9a00c7}{8})$$ `2x^3(x8)(x+8)` 
Question 2 of 4
2. Question
Factor.`3x^2y^23`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, find the Greatest Common Factor (GCF) of the two terms.Start by listing down their factors.Factors of `3x^2y^2`: `3``timesxtimesxtimesytimesy`Factors of `3`: `1times``3`Both `3x^2y^2` and `3` have `3` as their factor, so it is the GCF.Next, factor by placing `3` outside a bracket.Also, place the given polynomial inside the bracket with each term divided by `3`, then simplify.`3[(3x^2y^2div3)(3div3)]` `=` `3(x^2y^21)` Now, express both terms inside the parenthesis as perfect squares. In other words, both terms should have `2` as their exponent.`x^2y^21` `=` `(xy)^21` `(xy)^2=x^2y^2` `=` `(xy)^21^2` `1^2=1` Finally, label the values in the expression `(xy)^21^2` and substitute the values into the formula given for Factoring the Difference of Two Squares.`a=xy``b=1`$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$$ $$3[(\color{#00880A}{xy})^2\color{#9a00c7}{1}^2]$$ `=` $$3(\color{#00880A}{xy}\color{#9a00c7}{1})(\color{#00880A}{xy}+\color{#9a00c7}{1})$$ `3(xy1)(xy+1)` 
Question 3 of 4
3. Question
Factor.`m^481`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 inside the parenthesis as perfect squares. In other words, both terms should have `2` as their exponent.`m^481` `=` `(m^2)^281` `(m^2)^2=m^4` `=` `(m^2)^29^2` `9^2=81` Next, label the values in the expression `(m^2)^29^2` and substitute the values into the formula given for Factoring the Difference of Two Squares.`a=m^2``b=9`$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}\color{#9a00c7}{b})$$ $$(\color{#00880A}{m^2})^2\color{#9a00c7}{9}^2$$ `=` $$(\color{#00880A}{m^2}+\color{#9a00c7}{9})(\color{#00880A}{m^2}\color{#9a00c7}{9})$$ Now, express both terms inside the second parenthesis as perfect squares. In other words, both terms should have `2` as their exponent.`m^29` `=` `m^23^2` `3^2=9` Finally, label the values in the expression `m^23^2` and substitute the values into the formula given for Factoring the Difference of Two Squares.`a=m``b=3`$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$$ $$(m^2+9)(\color{#00880A}{m}^2\color{#9a00c7}{3}^2)$$ `=` $$(m^2+9)(\color{#00880A}{m}\color{#9a00c7}{3})(\color{#00880A}{m}+\color{#9a00c7}{3})$$ `(m^2+9)(m3)(m+3)` 
Question 4 of 4
4. Question
Factor.`16x^41`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 inside the parenthesis as perfect squares. In other words, both terms should have `2` as their exponent.`16x^41` `=` `(4x^2)^21` `(4x^2)^2=16x^4` `=` `(4x^2)^21^2` `1^2=1` Next, label the values in the expression `(4x^2)^21^2` and substitute the values into the formula given for Factoring the Difference of Two Squares.`a=4x^2``b=1`$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}\color{#9a00c7}{b})$$ $$(\color{#00880A}{4x^2})^2\color{#9a00c7}{1}^2$$ `=` $$(\color{#00880A}{4x^2}+\color{#9a00c7}{1})(\color{#00880A}{4x^2}\color{#9a00c7}{1})$$ Now, express both terms inside the second parenthesis as perfect squares. In other words, both terms should have `2` as their exponent.`4x^21` `=` `(2x)^21` `(2x)^2=4x^2` `=` `(2x)^21^2` `1^2=1` Finally, label the values in the expression `(2x)^21^2` and substitute the values into the formula given for Factoring the Difference of Two Squares.`a=2x``b=1`$$\color{#00880A}{a}^2\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$$ $$(4x^2+1)[(\color{#00880A}{2x})^2\color{#9a00c7}{1}^2]$$ `=` $$(4x^2+1)(\color{#00880A}{2x}\color{#9a00c7}{1})(\color{#00880A}{2x}+\color{#9a00c7}{1})$$ `(4x^2+1)(2x1)(2x+1)`
Quizzes
 Greatest Common Factor 1
 Greatest Common Factor 2
 Factor Expressions using GCF
 Factor Expressions 1
 Factor Expressions 2
 Factor Expressions with Negative Numbers
 Factor Difference of Two Squares 1
 Factor Difference of Two Squares 2
 Factor Difference of Two Squares 3
 Factor by Grouping
 Factor Difference of Two Squares (Harder) 1
 Factor Difference of Two Squares (Harder) 2
 Factor Difference of Two Squares (Harder) 3
 Factor Quadratics 1
 Factor Quadratics 2
 Factor Quadratics 3
 Factor Quadratics with Leading Coefficient more than 1 (1)
 Factor Quadratics with Leading Coefficient more than 1 (2)
 Factor Quadratics with Leading Coefficient more than 1 (3)
 Factor Quadratics (Complex)