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Difference of Two SquaresDifference of Two Squares
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Question 1 of 7
1. Question
Expand and simplify.`(x+13)(x-13)`Hint
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Incorrect
Difference of Two Squares
$$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})=\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$First, label the values in the given expression.$$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$$`(x+13)(x-13)``a=x``b=13`Substitute the values into the formula given for Difference of Two Squares.$$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$$ `=` $$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$ $$(\color{#00880A}{x}+\color{#9a00c7}{13})(\color{#00880A}{x}-\color{#9a00c7}{13})$$ `=` $$\color{#00880A}{x}^2-\color{#9a00c7}{13}^2$$ `=` `x^2-169` Simplify `x^2-169` -
Question 2 of 7
2. Question
Expand and simplify.`(9-f)(9+f)`Hint
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Correct!
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Difference of Two Squares
$$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})=\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$First, label the values in the given expression.$$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$$`(9-f)(9+f)``a=9``b=f`Substitute the values into the formula given for Difference of Two Squares.$$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$$ `=` $$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$ $$(\color{#00880A}{9}-\color{#9a00c7}{f})(\color{#00880A}{9}+\color{#9a00c7}{f})$$ `=` $$\color{#00880A}{9}^2-\color{#9a00c7}{f}^2$$ `=` `81-f^2` Simplify `81-f^2` -
Question 3 of 7
3. Question
Expand and simplify.`(3+4x)(3-4x)`Hint
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Difference of Two Squares
$$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})=\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$First, label the values in the given expression.$$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$$`(3+4x)(3-4x)``a=3``b=4x`Substitute the values into the formula given for Difference of Two Squares.$$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$$ `=` $$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$ $$(\color{#00880A}{3}+\color{#9a00c7}{4x})(\color{#00880A}{3}-\color{#9a00c7}{4x})$$ `=` $$\color{#00880A}{3}^2-(\color{#9a00c7}{4x})^2$$ `=` `9-16x^2` Simplify `9-16x^2` -
Question 4 of 7
4. Question
Expand and simplify.`(7a+8b)(7a-8b)`Hint
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Well Done!
Incorrect
Difference of Two Squares
$$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})=\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$First, label the values in the given expression.$$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$$`(7a+8b)(7a-8b)``a=7a``b=8b`Substitute the values into the formula given for Difference of Two Squares.$$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$$ `=` $$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$ $$(\color{#00880A}{7a}+\color{#9a00c7}{8b})(\color{#00880A}{7a}-\color{#9a00c7}{8b})$$ `=` $$(\color{#00880A}{7a})^2-(\color{#9a00c7}{8b})^2$$ `=` `49a^2-64b^2` Simplify `49a^2-64b^2` -
Question 5 of 7
5. Question
Expand and simplify.`(5ab-3)(5ab+3)`Hint
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Nice Job!
Incorrect
Difference of Two Squares
$$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})=\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$First, label the values in the given expression.$$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$$`(5ab-3)(5ab+3)``a=5ab``b=3`Substitute the values into the formula given for Difference of Two Squares.$$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$$ `=` $$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$ $$(\color{#00880A}{5ab}-\color{#9a00c7}{3})(\color{#00880A}{5ab}+\color{#9a00c7}{3})$$ `=` $$(\color{#00880A}{5ab})^2-\color{#9a00c7}{3}^2$$ `=` `25a^2b^2-9` Simplify `25a^2b^2-9` -
Question 6 of 7
6. Question
Expand and simplify.`(x/3-2)(x/3+2)`Hint
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Exceptional!
Incorrect
Difference of Two Squares
$$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})=\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$First, label the values in the given expression.$$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$$`(x/3-2)(x/3+2)``a=x/3``b=2`Substitute the values into the formula given for Difference of Two Squares.$$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$$ `=` $$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$ $$\left(\color{#00880A}{\frac{x}{3}}-\color{#9a00c7}{2}\right)\left(\color{#00880A}{\frac{x}{3}}+\color{#9a00c7}{2}\right)$$ `=` $$\left(\color{#00880A}{\frac{x}{3}}\right)^2-\color{#9a00c7}{2}^2$$ `=` `(x^2)/(3^2)-4` Simplify `=` `(x^2)/9-4` Simplify `(x^2)/9-4` -
Question 7 of 7
7. Question
Expand and simplify.`4(2x+3y)(2x-3y)`Hint
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Excellent!
Incorrect
Difference of Two Squares
$$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})=\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$First, focus on simplifying the brackets by using the Difference of Two Squares.Start by labelling the values in the brackets.$$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$$`4``(2x+3y)(2x-3y)``a=2x``b=3y`Substitute the values into the formula.$$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$$ `=` $$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$ $$\color{#6F6161}{4}(\color{#00880A}{2x}+\color{#9a00c7}{3y})(\color{#00880A}{2x}-\color{#9a00c7}{3y})$$ `=` $$\color{#6F6161}{4}\left((\color{#00880A}{2x})^2-(\color{#9a00c7}{3y})^2\right)$$ `=` `4``(4x^2-9y^2)` Simplify Finally, distribute `4` to each value inside the parenthesis`4``(4x^2-9y^2)` `=` `(``4``times4x^2)-(``4``times9y^2)` `=` `16x^2-36y^2` `16x^2-36y^2`