Difference of Two Squares

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Question 1 of 7

1. Question

Expand and simplify.

`(x+13)(x-13)`

`x^2-169`
`x^2-13`
`169x`
`169x^2`

Hint

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Correct

Great Work!

Incorrect

$$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})=\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$$

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)`

`81-f^2`
`18-f^2`
`81-2f`
`81f^2`

Hint

Help Video

Correct

Correct!

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.

$$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$$

`(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)`

`9-16x^2`
`6-18x^2`
`25x^2`
`9-12x^2`

Hint

Help Video

Correct

Keep Going!

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.

$$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$$

`(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)`

`49a^2-64b^2`
`49a^2b^2`
`64ab^2`
`14a^2-56b^2`

Hint

Help Video

Correct

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)`

`25a^2b^2-9`
`5a^2-9b^2`
`25a^2-9b^2`
`10a^2b^2-6`

Hint

Help Video

Correct

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)`

`(x^2)/9-4`
`(2x)/9-4`
`1/9-4x`
`9x^2-4`

Hint

Help Video

Correct

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)`

`16x^2-36y^2`
`4x^2-8y^2`
`4x^2-4y^2`
`8x^2-13y^2`

Hint

Help Video

Correct

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`

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