Expand Perfect Squares

Question 1 of 7

Expand and simplify.

{(x + 5)}^{2}

$(x+5)^2$

1. $x^{2} + 2 x + 5$ $x^2+2x+5$
2. $x^{2} + 5 x + 20$ $x^2+5x+20$
3. $x^{2} + 5 x + 25$ $x^2+5x+25$
4. $x^{2} + 10 x + 25$ $x^2+10x+25$

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Expanding Perfect Square Binomials

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

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

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

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

First, label the values in the given expression.

(a + b)^{2}

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

{(x + 5)}^{2}

$(x+5)^2$

a = x

$a=x$

b = 5

$b=5$

Substitute the values into the formula given for Expanding Perfect Square Binomials.

$(\color{#00880A}{a}+\color{#9a00c7}{b})^2$	$=$ $=$	$\color{#00880A}{a}^2+2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$
$(\color{#00880A}{x}+\color{#9a00c7}{5})^2$	$=$ $=$	$\color{#00880A}{x}^2+2(\color{#00880A}{x})(\color{#9a00c7}{5})+\color{#9a00c7}{5}^2$
	$=$ $=$	$x^{2} + 10 x + 25$ $x^2+10x+25$	Simplify

x^{2} + 10 x + 25

$x^2+10x+25$

Question 2 of 7

Expand and simplify.

{(3 m + 2)}^{2}

$(3m+2)^2$

1. $3 m^{2} + 4 m + 4$ $3m^2+4m+4$
2. $6 m^{2} + 4 m + 2$ $6m^2+4m+2$
3. $3 m^{2} + 6 m + 4$ $3m^2+6m+4$
4. $9 m^{2} + 12 m + 4$ $9m^2+12m+4$

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Expanding Perfect Square Binomials

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

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

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

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

First, label the values in the given expression.

(a + b)^{2}

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

{(3 m + 2)}^{2}

$(3m+2)^2$

a = 3 m

$a=3m$

b = 2

$b=2$

Substitute the values into the formula given for Expanding Perfect Square Binomials.

$(\color{#00880A}{a}+\color{#9a00c7}{b})^2$	$=$ $=$	$\color{#00880A}{a}^2+2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$
$(\color{#00880A}{3m}+\color{#9a00c7}{2})^2$	$=$ $=$	$\color{#00880A}{3m}^2+2(\color{#00880A}{3m})(\color{#9a00c7}{2})+\color{#9a00c7}{2}^2$
	$=$ $=$	$9 m^{2} + 12 m + 4$ $9m^2+12m+4$	Simplify

9 m^{2} + 12 m + 4

$9m^2+12m+4$

Question 3 of 7

Expand and simplify.

{(a b - 4 c)}^{2}

$(ab-4c)^2$

1. $a^{2} b^{2} - 8 a b c + 16 c^{2}$ $a^2 b^2-8abc+16c^2$
2. $a b^{2} - 8 a b c + 16 c^{2}$ $ab^2-8abc+16c^2$
3. $a b^{2} - 4 a b c + 8 c^{2}$ $ab^2-4abc+8c^2$
4. $a^{2} b^{2} - 16 a b c + 8 c^{2}$ $a^2 b^2-16abc+8c^2$

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Expanding Perfect Square Binomials

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

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

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

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

First, label the values in the given expression.

(a - b)^{2}

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

{(a b - 4 c)}^{2}

$(ab-4c)^2$

a = a b

$a=ab$

b = 4 c

$b=4c$

Substitute the values into the formula given for Expanding Perfect Square Binomials.

$(\color{#00880A}{a}-\color{#9a00c7}{b})^2$	$=$ $=$	$\color{#00880A}{a}^2-2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$
$(\color{#00880A}{ab}-\color{#9a00c7}{4c})^2$	$=$ $=$	$(\color{#00880A}{ab})^2-2(\color{#00880A}{ab})(\color{#9a00c7}{4c})+(\color{#9a00c7}{4c})^2$
	$=$ $=$	$a^{2} b^{2} - 8 a b c + 16 c^{2}$ $a^2 b^2-8abc+16c^2$	Simplify

a^{2} b^{2} - 8 a b c + 16 c^{2}

$a^2 b^2-8abc+16c^2$

Question 4 of 7

Expand and simplify.

{(2 t + 9)}^{2}

$(2t+9)^2$

1. $2 t^{2} + 18 t + 18$ $2t^2+18t+18$
2. $4 t^{2} + 20 t + 81$ $4t^2+20t+81$
3. $4 t^{2} + 24 t + 18$ $4t^2+24t+18$
4. $4 t^{2} + 36 t + 81$ $4t^2+36t+81$

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Expanding Perfect Square Binomials

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

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

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

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

First, label the values in the given expression.

(a + b)^{2}

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

{(2 t + 9)}^{2}

$(2t+9)^2$

a = 2 t

$a=2t$

b = 9

$b=9$

Substitute the values into the formula given for Expanding Perfect Square Binomials.

$(\color{#00880A}{a}+\color{#9a00c7}{b})^2$	$=$ $=$	$\color{#00880A}{a}^2+2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$
$(\color{#00880A}{2t}+\color{#9a00c7}{9})^2$	$=$ $=$	$\color{#00880A}{2t}^2+2(\color{#00880A}{2t})(\color{#9a00c7}{9})+\color{#9a00c7}{9}^2$
	$=$ $=$	$4 t^{2} + 36 t + 81$ $4t^2+36t+81$	Simplify

4 t^{2} + 36 t + 81

$4t^2+36t+81$

Question 5 of 7

Expand and simplify.

{(6 a - 5)}^{2}

$(6a-5)^2$

1. $24 a^{2} - 30 a + 25$ $24a^2-30a+25$
2. $36 a^{2} + 60 a - 25$ $36a^2+60a-25$
3. $12 a^{2} - 30 a + 25$ $12a^2-30a+25$
4. $36 a^{2} - 60 a + 25$ $36a^2-60a+25$

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Expanding Perfect Square Binomials

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

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

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

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

First, label the values in the given expression.

(a - b)^{2}

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

{(6 a - 5)}^{2}

$(6a-5)^2$

a = 6 a

$a=6a$

b = 5

$b=5$

Substitute the values into the formula given for Expanding Perfect Square Binomials.

$(\color{#00880A}{a}-\color{#9a00c7}{b})^2$	$=$ $=$	$\color{#00880A}{a}^2-2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$
$(\color{#00880A}{6a}-\color{#9a00c7}{5})^2$	$=$ $=$	$(\color{#00880A}{6a})^2-2(\color{#00880A}{6a})(\color{#9a00c7}{5})+(\color{#9a00c7}{5})^2$
	$=$ $=$	$36 a^{2} - 60 a + 25$ $36a^2-60a+25$	Simplify

36 a^{2} - 60 a + 25

$36a^2-60a+25$

Question 6 of 7

Expand and simplify.

{(a + \frac{1}{4})}^{2}

$(a+1/4)^2$

1. $2 a^{2} + 2 a + \frac{1}{16}$ $2a^2+2a+1/(16)$
2. $a^{2} + \frac{a}{4} + \frac{1}{8}$ $a^2+a/4+1/8$
3. $a^{2} + 2 a + \frac{1}{4}$ $a^2+2a+1/4$
4. $a^{2} + \frac{a}{2} + \frac{1}{16}$ $a^2+a/2+1/(16)$

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Expanding Perfect Square Binomials

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

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

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

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

First, label the values in the given expression.

(a + b)^{2}

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

{(a + \frac{1}{4})}^{2}

$(a+1/4)^2$

a = a

$a=a$

b = \frac{1}{4}

$b=1/4$

Substitute the values into the formula given for Expanding Perfect Square Binomials.

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

$\left(\color{#00880A}{a}+\color{#9a00c7}{\frac{1}{4}}\right)^2$	$=$ $=$	$\color{#00880A}{a}^2+2(\color{#00880A}{a})\left(\color{#9a00c7}{\frac{1}{4}}\right)+\color{#9a00c7}{\frac{1}{4}}^2$
	$=$ $=$	$a^{2} + \frac{a}{2} + \frac{1}{{(4)}^{2}}$ $a^2+a/2+1/((4)^2)$	Simplify

	$=$ $=$	$a^{2} + \frac{a}{2} + \frac{1}{16}$ $a^2+a/2+1/(16)$	Simplify

a^{2} + \frac{a}{2} + \frac{1}{16}

$a^2+a/2+1/(16)$

Question 7 of 7

Expand and simplify.

{(2 y - \frac{3}{y})}^{2}

$(2y-3/y)^2$

1. $8 y^{2} + 12 + \frac{3}{y^{2}}$ $8y^2+12+3/(y^2)$
2. $4y^2-7a+9/y$
3. $2y^2-12a+3/y$
4. $4y^2-12+9/(y^2)$

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Expanding Perfect Square Binomials

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

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

First, label the values in the given expression.

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

$(2y-3/y)^2$

$a=2y$

$b=3/y$

Substitute the values into the formula given for Expanding Perfect Square Binomials.

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

$\left(\color{#00880A}{2y}-\color{#9a00c7}{\frac{3}{y}}\right)^2$	$=$	$\color{#00880A}{2y}^2-2(\color{#00880A}{2y})\left(\color{#9a00c7}{\frac{3}{y}}\right)+\color{#9a00c7}{\frac{3}{y}}^2$
	$=$	$4y^2-2(2times3)+((3)^2)/((y)^2)$	$ytimes1/y$ cancels out`

	$=$	$4y^2-12+9/(y^2)$	Simplify

$4y^2-12+9/(y^2)$

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