Basic Math Examples

${(b - 4)}^{2} + b \cdot 5 + \frac{36}{b}$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(b - 4)}^{2}$ as $(b - 4) (b - 4)$ .

$(b - 4) (b - 4) + b \cdot 5 + \frac{36}{b}$

Step 1.2

Expand $(b - 4) (b - 4)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$b (b - 4) - 4 (b - 4) + b \cdot 5 + \frac{36}{b}$

Step 1.2.2

Apply the distributive property.

$b \cdot b + b \cdot - 4 - 4 (b - 4) + b \cdot 5 + \frac{36}{b}$

Step 1.2.3

Apply the distributive property.

$b \cdot b + b \cdot - 4 - 4 b - 4 \cdot - 4 + b \cdot 5 + \frac{36}{b}$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $b$ by $b$ .

$b^{2} + b \cdot - 4 - 4 b - 4 \cdot - 4 + b \cdot 5 + \frac{36}{b}$

Step 1.3.1.2

Move $- 4$ to the left of $b$ .

$b^{2} - 4 \cdot b - 4 b - 4 \cdot - 4 + b \cdot 5 + \frac{36}{b}$

Step 1.3.1.3

Multiply $- 4$ by $- 4$ .

$b^{2} - 4 b - 4 b + 16 + b \cdot 5 + \frac{36}{b}$

Step 1.3.2

Subtract $4 b$ from $- 4 b$ .

$b^{2} - 8 b + 16 + b \cdot 5 + \frac{36}{b}$

Step 1.4

Move $5$ to the left of $b$ .

$b^{2} - 8 b + 16 + 5 b + \frac{36}{b}$

Step 2

Find the common denominator.

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Step 2.1

Write $b^{2}$ as a fraction with denominator $1$ .

$\frac{b^{2}}{1} - 8 b + 16 + 5 b + \frac{36}{b}$

Step 2.2

Multiply $\frac{b^{2}}{1}$ by $\frac{b}{b}$ .

$\frac{b^{2}}{1} \cdot \frac{b}{b} - 8 b + 16 + 5 b + \frac{36}{b}$

Step 2.3

Multiply $\frac{b^{2}}{1}$ by $\frac{b}{b}$ .

$\frac{b^{2} b}{b} - 8 b + 16 + 5 b + \frac{36}{b}$

Step 2.4

Write $- 8 b$ as a fraction with denominator $1$ .

$\frac{b^{2} b}{b} + \frac{- 8 b}{1} + 16 + 5 b + \frac{36}{b}$

Step 2.5

Multiply $\frac{- 8 b}{1}$ by $\frac{b}{b}$ .

$\frac{b^{2} b}{b} + \frac{- 8 b}{1} \cdot \frac{b}{b} + 16 + 5 b + \frac{36}{b}$

Step 2.6

Multiply $\frac{- 8 b}{1}$ by $\frac{b}{b}$ .

$\frac{b^{2} b}{b} + \frac{- 8 b \cdot b}{b} + 16 + 5 b + \frac{36}{b}$

Step 2.7

Write $16$ as a fraction with denominator $1$ .

$\frac{b^{2} b}{b} + \frac{- 8 b \cdot b}{b} + \frac{16}{1} + 5 b + \frac{36}{b}$

Step 2.8

Multiply $\frac{16}{1}$ by $\frac{b}{b}$ .

$\frac{b^{2} b}{b} + \frac{- 8 b \cdot b}{b} + \frac{16}{1} \cdot \frac{b}{b} + 5 b + \frac{36}{b}$

Step 2.9

Multiply $\frac{16}{1}$ by $\frac{b}{b}$ .

$\frac{b^{2} b}{b} + \frac{- 8 b \cdot b}{b} + \frac{16 b}{b} + 5 b + \frac{36}{b}$

Step 2.10

Write $5 b$ as a fraction with denominator $1$ .

$\frac{b^{2} b}{b} + \frac{- 8 b \cdot b}{b} + \frac{16 b}{b} + \frac{5 b}{1} + \frac{36}{b}$

Step 2.11

Multiply $\frac{5 b}{1}$ by $\frac{b}{b}$ .

$\frac{b^{2} b}{b} + \frac{- 8 b \cdot b}{b} + \frac{16 b}{b} + \frac{5 b}{1} \cdot \frac{b}{b} + \frac{36}{b}$

Step 2.12

Multiply $\frac{5 b}{1}$ by $\frac{b}{b}$ .

$\frac{b^{2} b}{b} + \frac{- 8 b \cdot b}{b} + \frac{16 b}{b} + \frac{5 b \cdot b}{b} + \frac{36}{b}$

Step 3

Combine the numerators over the common denominator.

$\frac{b^{2} b - 8 b \cdot b + 16 b + 5 b \cdot b + 36}{b}$

Step 4

Simplify each term.

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Step 4.1

Multiply $b^{2}$ by $b$ by adding the exponents.

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Step 4.1.1

Multiply $b^{2}$ by $b$ .

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Step 4.1.1.1

Raise $b$ to the power of $1$ .

$\frac{b^{2} b^{1} - 8 b \cdot b + 16 b + 5 b \cdot b + 36}{b}$

Step 4.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{b^{2 + 1} - 8 b \cdot b + 16 b + 5 b \cdot b + 36}{b}$

Step 4.1.2

Add $2$ and $1$ .

$\frac{b^{3} - 8 b \cdot b + 16 b + 5 b \cdot b + 36}{b}$

Step 4.2

Multiply $b$ by $b$ by adding the exponents.

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Step 4.2.1

Move $b$ .

$\frac{b^{3} - 8 (b \cdot b) + 16 b + 5 b \cdot b + 36}{b}$

Step 4.2.2

Multiply $b$ by $b$ .

$\frac{b^{3} - 8 b^{2} + 16 b + 5 b \cdot b + 36}{b}$

Step 4.3

Multiply $b$ by $b$ by adding the exponents.

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Step 4.3.1

Move $b$ .

$\frac{b^{3} - 8 b^{2} + 16 b + 5 (b \cdot b) + 36}{b}$

Step 4.3.2

Multiply $b$ by $b$ .

$\frac{b^{3} - 8 b^{2} + 16 b + 5 b^{2} + 36}{b}$

Step 5

Add $- 8 b^{2}$ and $5 b^{2}$ .

$\frac{b^{3} - 3 b^{2} + 16 b + 36}{b}$