Basic Math Examples

$\frac{(- 3 - 2 {(- 4 + h)}^{2}) - (- 3 - 2 {(- 4)}^{2})}{h}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite

${(- 4 + h)}^{2}$ as

$(- 4 + h) (- 4 + h)$ .

$\frac{- 3 - 2 ((- 4 + h) (- 4 + h)) - (- 3 - 2 {(- 4)}^{2})}{h}$

Step 1.2

Expand

$(- 4 + h) (- 4 + h)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$\frac{- 3 - 2 (- 4 (- 4 + h) + h (- 4 + h)) - (- 3 - 2 {(- 4)}^{2})}{h}$

Step 1.2.2

Apply the distributive property.

$\frac{- 3 - 2 (- 4 \cdot - 4 - 4 h + h (- 4 + h)) - (- 3 - 2 {(- 4)}^{2})}{h}$

Step 1.2.3

Apply the distributive property.

$\frac{- 3 - 2 (- 4 \cdot - 4 - 4 h + h \cdot - 4 + h \cdot h) - (- 3 - 2 {(- 4)}^{2})}{h}$

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

$- 4$ by

$- 4$ .

$\frac{- 3 - 2 (16 - 4 h + h \cdot - 4 + h \cdot h) - (- 3 - 2 {(- 4)}^{2})}{h}$

Step 1.3.1.2

Move

$- 4$ to the left of

$h$ .

$\frac{- 3 - 2 (16 - 4 h - 4 \cdot h + h \cdot h) - (- 3 - 2 {(- 4)}^{2})}{h}$

Step 1.3.1.3

Multiply

$h$ by

$h$ .

$\frac{- 3 - 2 (16 - 4 h - 4 h + h^{2}) - (- 3 - 2 {(- 4)}^{2})}{h}$

Step 1.3.2

Subtract

$4 h$ from

$- 4 h$ .

$\frac{- 3 - 2 (16 - 8 h + h^{2}) - (- 3 - 2 {(- 4)}^{2})}{h}$

Step 1.4

Apply the distributive property.

$\frac{- 3 - 2 \cdot 16 - 2 (- 8 h) - 2 h^{2} - (- 3 - 2 {(- 4)}^{2})}{h}$

Step 1.5

Simplify.

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Step 1.5.1

Multiply

$- 2$ by

$16$ .

$\frac{- 3 - 32 - 2 (- 8 h) - 2 h^{2} - (- 3 - 2 {(- 4)}^{2})}{h}$

Step 1.5.2

Multiply

$- 8$ by

$- 2$ .

$\frac{- 3 - 32 + 16 h - 2 h^{2} - (- 3 - 2 {(- 4)}^{2})}{h}$

Step 1.6

Simplify each term.

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Step 1.6.1

Raise

$- 4$ to the power of

$2$ .

$\frac{- 3 - 32 + 16 h - 2 h^{2} - (- 3 - 2 \cdot 16)}{h}$

Step 1.6.2

Multiply

$- 2$ by

$16$ .

$\frac{- 3 - 32 + 16 h - 2 h^{2} - (- 3 - 32)}{h}$

Step 1.7

Subtract

$32$ from

$- 3$ .

$\frac{- 3 - 32 + 16 h - 2 h^{2} - - 35}{h}$

Step 1.8

Multiply

$- 1$ by

$- 35$ .

$\frac{- 3 - 32 + 16 h - 2 h^{2} + 35}{h}$

Step 1.9

Subtract

$32$ from

$- 3$ .

$\frac{- 35 + 16 h - 2 h^{2} + 35}{h}$

Step 1.10

Add

$- 35$ and

$35$ .

$\frac{16 h - 2 h^{2} + 0}{h}$

Step 1.11

Add

$16 h - 2 h^{2}$ and

$0$ .

$\frac{16 h - 2 h^{2}}{h}$

Step 1.12

Factor

$2 h$ out of

$16 h - 2 h^{2}$ .

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Step 1.12.1

Factor

$2 h$ out of

$16 h$ .

$\frac{2 h (8) - 2 h^{2}}{h}$

Step 1.12.2

Factor

$2 h$ out of

$- 2 h^{2}$ .

$\frac{2 h (8) + 2 h (- h)}{h}$

Step 1.12.3

Factor

$2 h$ out of

$2 h (8) + 2 h (- h)$ .

$\frac{2 h (8 - h)}{h}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of

$h$ .

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Step 2.1.1

Cancel the common factor.

$\frac{2 h (8 - h)}{h}$

Step 2.1.2

Divide

$2 (8 - h)$ by

$1$ .

$2 (8 - h)$

Step 2.2

Apply the distributive property.

$2 \cdot 8 + 2 (- h)$

Step 2.3

Multiply.

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Step 2.3.1

Multiply

$2$ by

$8$ .

$16 + 2 (- h)$

Step 2.3.2

Multiply

$- 1$ by

$2$ .

$16 - 2 h$