Difference of Two Squares

Question 1 of 7

Expand and simplify.

(x + 13) (x - 13)

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

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

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

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

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

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

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

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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)

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

$a=x/3$

$b=2$

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

Expand and simplify.

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

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

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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, 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

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