Calculus Examples

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

Step 1

Remove parentheses.

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

Step 2

Regroup terms.

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

Step 3

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

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

Step 4

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

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Step 4.1

Apply the distributive property.

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

Step 4.2

Apply the distributive property.

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

Step 4.3

Apply the distributive property.

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

Step 5

Simplify and combine like terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply $- 4$ by $- 4$ .

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

Step 5.1.2

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

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

Step 5.1.3

Multiply $h$ by $h$ .

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

Step 5.2

Subtract $4 h$ from $- 4 h$ .

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

Step 6

Add $- 8 h$ and $h$ .

$16 + h^{2} - 7 h - 4 - ({(- 4)}^{2} - 4)$

Step 7

Reorder terms.

$h^{2} - 7 h + 16 - 4 - ({(- 4)}^{2} - 4)$

Step 8

Raise $- 4$ to the power of $2$ .

$h^{2} - 7 h + 16 - 4 - (16 - 4)$

Step 9

Subtract $4$ from $16$ .

$h^{2} - 7 h + 16 - 4 - 1 \cdot 12$

Step 10

Multiply $- 1$ by $12$ .

$h^{2} - 7 h + 16 - 4 - 12$

Step 11

Subtract $12$ from $- 4$ .

$h^{2} - 7 h + 16 - 16$

Step 12

Subtract $16$ from $16$ .

$h^{2} - 7 h + 0$

Step 13

Add $h^{2} - 7 h$ and $0$ .

$h^{2} - 7 h$

Step 14

Factor $h$ out of $h^{2} - 7 h$ .

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Step 14.1

Factor $h$ out of $h^{2}$ .

$h \cdot h - 7 h$

Step 14.2

Factor $h$ out of $- 7 h$ .

$h \cdot h + h \cdot - 7$

Step 14.3

Factor $h$ out of $h \cdot h + h \cdot - 7$ .

$h (h - 7)$