Difference of Two Squares

Question 1 of 7

Expand and simplify.

(x + 13) (x - 13)

$(x+13)(x-13)$

1. $x^{2} - 169$ $x^2-169$
2. $169 x^{2}$ $169x^2$
3. $x^{2} - 13$ $x^2-13$
4. $169 x$ $169x$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Difference of Two Squares

(a + b) (a - b) = a^{2} - b^{2}

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

First, label the values in the given expression.

(a + b) (a - b)

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

(x + 13) (x - 13)

$(x+13)(x-13)$

a = x

$a=x$

b = 13

$b=13$

Substitute the values into the formula given for Difference of Two Squares.

$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$	$=$ $=$	$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$
$(\color{#00880A}{x}+\color{#9a00c7}{13})(\color{#00880A}{x}-\color{#9a00c7}{13})$	$=$ $=$	$\color{#00880A}{x}^2-\color{#9a00c7}{13}^2$
	$=$ $=$	$x^{2} - 169$ $x^2-169$	Simplify

x^{2} - 169

$x^2-169$

Question 2 of 7

Expand and simplify.

(9 - f) (9 + f)

$(9-f)(9+f)$

1. $81 f^{2}$ $81f^2$
2. $81 - f^{2}$ $81-f^2$
3. $18 - f^{2}$ $18-f^2$
4. $81 - 2 f$ $81-2f$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Difference of Two Squares

(a - b) (a + b) = a^{2} - b^{2}

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

First, label the values in the given expression.

(a - b) (a + b)

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

(9 - f) (9 + f)

$(9-f)(9+f)$

a = 9

$a=9$

b = f

$b=f$

Substitute the values into the formula given for Difference of Two Squares.

$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$	$=$ $=$	$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$
$(\color{#00880A}{9}-\color{#9a00c7}{f})(\color{#00880A}{9}+\color{#9a00c7}{f})$	$=$ $=$	$\color{#00880A}{9}^2-\color{#9a00c7}{f}^2$
	$=$ $=$	$81 - f^{2}$ $81-f^2$	Simplify

81 - f^{2}

$81-f^2$

Question 3 of 7

Expand and simplify.

(3 + 4 x) (3 - 4 x)

$(3+4x)(3-4x)$

1. $9 - 12 x^{2}$ $9-12x^2$
2. $9 - 16 x^{2}$ $9-16x^2$
3. $6 - 18 x^{2}$ $6-18x^2$
4. $25 x^{2}$ $25x^2$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Difference of Two Squares

(a + b) (a - b) = a^{2} - b^{2}

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

First, label the values in the given expression.

(a + b) (a - b)

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

(3 + 4 x) (3 - 4 x)

$(3+4x)(3-4x)$

a = 3

$a=3$

b = 4 x

$b=4x$

Substitute the values into the formula given for Difference of Two Squares.

$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$	$=$ $=$	$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$
$(\color{#00880A}{3}+\color{#9a00c7}{4x})(\color{#00880A}{3}-\color{#9a00c7}{4x})$	$=$ $=$	$\color{#00880A}{3}^2-(\color{#9a00c7}{4x})^2$
	$=$ $=$	$9 - 16 x^{2}$ $9-16x^2$	Simplify

9 - 16 x^{2}

$9-16x^2$

Question 4 of 7

Expand and simplify.

(7 a + 8 b) (7 a - 8 b)

$(7a+8b)(7a-8b)$

1. $49 a^{2} - 64 b^{2}$ $49a^2-64b^2$
2. $64 a b^{2}$ $64ab^2$
3. $49 a^{2} b^{2}$ $49a^2b^2$
4. $14 a^{2} - 56 b^{2}$ $14a^2-56b^2$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Difference of Two Squares

(a + b) (a - b) = a^{2} - b^{2}

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

First, label the values in the given expression.

(a + b) (a - b)

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

(7 a + 8 b) (7 a - 8 b)

$(7a+8b)(7a-8b)$

a = 7 a

$a=7a$

b = 8 b

$b=8b$

Substitute the values into the formula given for Difference of Two Squares.

$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$	$=$ $=$	$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$
$(\color{#00880A}{7a}+\color{#9a00c7}{8b})(\color{#00880A}{7a}-\color{#9a00c7}{8b})$	$=$ $=$	$(\color{#00880A}{7a})^2-(\color{#9a00c7}{8b})^2$
	$=$ $=$	$49 a^{2} - 64 b^{2}$ $49a^2-64b^2$	Simplify

49 a^{2} - 64 b^{2}

$49a^2-64b^2$

Question 5 of 7

Expand and simplify.

(5 a b - 3) (5 a b + 3)

$(5ab-3)(5ab+3)$

1. $5 a^{2} - 9 b^{2}$ $5a^2-9b^2$
2. $25 a^{2} - 9 b^{2}$ $25a^2-9b^2$
3. $25 a^{2} b^{2} - 9$ $25a^2b^2-9$
4. $10 a^{2} b^{2} - 6$ $10a^2b^2-6$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Difference of Two Squares

(a - b) (a + b) = a^{2} - b^{2}

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

First, label the values in the given expression.

(a - b) (a + b)

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

(5 a b - 3) (5 a b + 3)

$(5ab-3)(5ab+3)$

a = 5 a b

$a=5ab$

b = 3

$b=3$

Substitute the values into the formula given for Difference of Two Squares.

$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$	$=$ $=$	$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$
$(\color{#00880A}{5ab}-\color{#9a00c7}{3})(\color{#00880A}{5ab}+\color{#9a00c7}{3})$	$=$ $=$	$(\color{#00880A}{5ab})^2-\color{#9a00c7}{3}^2$
	$=$ $=$	$25 a^{2} b^{2} - 9$ $25a^2b^2-9$	Simplify

25 a^{2} b^{2} - 9

$25a^2b^2-9$

Question 6 of 7

Expand and simplify.

(\frac{x}{3} - 2) (\frac{x}{3} + 2)

$(x/3-2)(x/3+2)$

1. $\frac{1}{9} - 4 x$ $1/9-4x$
2. $\frac{2 x}{9} - 4$ $(2x)/9-4$
3. $\frac{x^{2}}{9} - 4$ $(x^2)/9-4$
4. $9 x^{2} - 4$ $9x^2-4$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Difference of Two Squares

(a - b) (a + b) = a^{2} - b^{2}

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

First, label the values in the given expression.

(a - b) (a + b)

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

(\frac{x}{3} - 2) (\frac{x}{3} + 2)

$(x/3-2)(x/3+2)$

a = \frac{x}{3}

$a=x/3$

b = 2

$b=2$

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

Expand and simplify.

$4(2x+3y)(2x-3y)$

1. $8x^2-13y^2$
2. $16x^2-36y^2$
3. $4x^2-8y^2$
4. $4x^2-4y^2$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

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

$4$ $(4x^2-9y^2)$	$=$	$($ $4$ $times4x^2)-($ $4$ $times9y^2)$
	$=$	$16x^2-36y^2$

$16x^2-36y^2$

Difference of Two Squares

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Great Work!

Difference of Two Squares

2. Question

Hint

Correct!

Difference of Two Squares

3. Question

Hint

Keep Going!

Difference of Two Squares

4. Question

Hint

Well Done!

Difference of Two Squares

5. Question

Hint

Nice Job!

Difference of Two Squares

6. Question

Hint

Exceptional!

Difference of Two Squares

7. Question

Hint

Excellent!

Difference of Two Squares

Quizzes