Calculus Examples

$- 3 - 8 {(a + h)}^{2}$

Step 1

Simplify each term.

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Step 1.1

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

$- 3 - 8 ((a + h) (a + h))$

Step 1.2

Expand $(a + h) (a + h)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$- 3 - 8 (a (a + h) + h (a + h))$

Step 1.2.2

Apply the distributive property.

$- 3 - 8 (a \cdot a + a h + h (a + h))$

Step 1.2.3

Apply the distributive property.

$- 3 - 8 (a \cdot a + a h + h a + h \cdot h)$

$- 3 - 8 (a \cdot a + a h + h a + h \cdot h)$

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 $a$ by $a$ .

$- 3 - 8 (a^{2} + a h + h a + h \cdot h)$

Step 1.3.1.2

Multiply $h$ by $h$ .

$- 3 - 8 (a^{2} + a h + h a + h^{2})$

$- 3 - 8 (a^{2} + a h + h a + h^{2})$

Step 1.3.2

Add $a h$ and $h a$ .

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Step 1.3.2.1

Reorder $h$ and $a$ .

$- 3 - 8 (a^{2} + a h + a h + h^{2})$

Step 1.3.2.2

Add $a h$ and $a h$ .

$- 3 - 8 (a^{2} + 2 a h + h^{2})$

$- 3 - 8 (a^{2} + 2 a h + h^{2})$

$- 3 - 8 (a^{2} + 2 a h + h^{2})$

Step 1.4

Apply the distributive property.

$- 3 - 8 a^{2} - 8 (2 a h) - 8 h^{2}$

Step 1.5

Multiply $2$ by $- 8$ .

$- 3 - 8 a^{2} - 16 a h - 8 h^{2}$

$- 3 - 8 a^{2} - 16 a h - 8 h^{2}$

Step 2

Move $- 3$ .

$- 8 a^{2} - 16 a h - 8 h^{2} - 3$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$