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Factor Difference of Two Squares (Harder) 1Factor Difference of Two Squares (Harder) 1
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Question 1 of 5
1. Question
Factor.`2y^2-18`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 `2y^2`: `2``timesytimesy`Factors of `18`: `2``times9`Both `2y^2` and `18` have `2` as their factor, so it is the GCF.Next, factor by placing `2` outside a bracket.Also, place the given polynomial inside the bracket with each term divided by `2`, then simplify.`2[(2y^2div2)-(18div2)]` `=` `2(y^2-9)` Now, express both terms inside the parenthesis as perfect squares. In other words, both terms should have `2` as their exponent.`y^2-9` `=` `y^2-3^2` `3^2=9` Finally, label the values in the expression `2y^2-18` and substitute the values into the formula given for Factoring the Difference of Two Squares.`a=y``b=3`$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$$ $$2(\color{#00880A}{y}^2-\color{#9a00c7}{3}^2)$$ `=` $$2(\color{#00880A}{y}-\color{#9a00c7}{3})(\color{#00880A}{y}+\color{#9a00c7}{3})$$ `2(y-3)(y+3)` -
Question 2 of 5
2. Question
Factor.`5x^2-500`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 `5x^2`: `5``timesxtimesx`Factors of `500`: `5``times100`Both `5x^2` and `500` have `5` as their factor, so it is the GCF.Next, factor by placing `5` outside a bracket.Also, place the given polynomial inside the bracket with each term divided by `5`, then simplify.`5[(5x^2div5)-(500div5)]` `=` `5(x^2-100)` Now, express both terms inside the parenthesis as perfect squares. In other words, both terms should have `2` as their exponent.`x^2-100` `=` `x^2-10^2` `10^2=100` Finally, label the values in the expression `5x^2-500` and substitute the values into the formula given for Factoring the Difference of Two Squares.`a=x``b=10`$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$$ $$5(\color{#00880A}{x}^2-\color{#9a00c7}{10}^2)$$ `=` $$5(\color{#00880A}{x}-\color{#9a00c7}{10})(\color{#00880A}{x}+\color{#9a00c7}{10})$$ `5(x-10)(x+10)` -
Question 3 of 5
3. Question
Factor.`63-7b^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, find the Greatest Common Factor (GCF) of the two terms.Start by listing down their factors.Factors of `63`: `7``times9`Factors of `7b^2`: `7``timesbtimesb`Both `63` and `7b^2` have `7` as their factor, so it is the GCF.Next, factor by placing `7` outside a bracket.Also, place the given polynomial inside the bracket with each term divided by `7`, then simplify.`7[(63div7)-(7b^2div7)]` `=` `7(9-b^2)` Now, express both terms inside the parenthesis as perfect squares. In other words, both terms should have `2` as their exponent.`9-b^2` `=` `3^2-b^2` `3^2=9` Finally, label the values in the expression `63-7b^2` and substitute the values into the formula given for Factoring the Difference of Two Squares.`a=3``b=b`$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$$ $$7(\color{#00880A}{3}^2-\color{#9a00c7}{b}^2)$$ `=` $$7(\color{#00880A}{3}-\color{#9a00c7}{b})(\color{#00880A}{3}+\color{#9a00c7}{b})$$ `7(3-b)(3+b)` -
Question 4 of 5
4. Question
Factor.`54m^3-24m`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 `54m^3`: `6``times9times``m``timesmtimesm`Factors of `24m`: `4times``6``times``m`Collect the common factors and multiply them all to get the GCF.GCF `=` `6``times``m` `=` `6m` Next, factor by placing `6m` outside a bracket.Also, place the given polynomial inside the bracket with each term divided by `6m`, then simplify.`6m[(54m^3div6m)-(24mdiv6m)]` `=` `6m(9m^2-4)` Now, express both terms inside the parenthesis as perfect squares. In other words, both terms should have `2` as their exponent.`9m^2-4` `=` `(3m)^2-4` `(3m)^2=9m^2` `=` `(3m)^2-2^2` `2^2=4` Finally, label the values in the expression `54m^3-24m` and substitute the values into the formula given for Factoring the Difference of Two Squares.`a=3m``b=4`$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$$ $$6m[(\color{#00880A}{3m})^2-\color{#9a00c7}{2}^2]$$ `=` $$6m(\color{#00880A}{3m}-\color{#9a00c7}{2})(\color{#00880A}{3m}+\color{#9a00c7}{2})$$ `6m(3m-2)(3m+2)` -
Question 5 of 5
5. Question
Factor.`72x-32x^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 `72x`: `8``times9times``x``Factors of `32x^3`: `4times``8``times``x``timesxtimesx`Collect the common factors and multiply them all to get the GCF.GCF `=` `8``times``x` `=` `8x` Next, factor by placing `8x` outside a bracket.Also, place the given polynomial inside the bracket with each term divided by `8x`, then simplify.`8x[(72xdiv8x)-(32x^3div8x)]` `=` `8x(9-4x^2)` Now, express both terms inside the parenthesis as perfect squares. In other words, both terms should have `2` as their exponent.`9-4x^2` `=` `3^2-4x^2` `3^2=9` `=` `3^2-(2x)^2` `(2x)^2=4x^2` Finally, label the values in the expression `72x-32x^3` and substitute the values into the formula given for Factoring the Difference of Two Squares.`a=3``b=2x`$$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$ `=` $$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$$ $$8x[\color{#00880A}{3}^2-(\color{#9a00c7}{2x})^2]$$ `=` $$8x(\color{#00880A}{3}-\color{#9a00c7}{2x})(\color{#00880A}{3}+\color{#9a00c7}{2x})$$ `8x(3-2x)(3+2x)`
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)