Calculus Examples

$6 {(a + h)}^{2} - 14 (a + h) + 7$

Step 1

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

$6 ((a + h) (a + h)) - 14 (a + h) + 7$

Step 2

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

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Step 2.1

Apply the distributive property.

$6 (a (a + h) + h (a + h)) - 14 (a + h) + 7$

Step 2.2

Apply the distributive property.

$6 (a \cdot a + a h + h (a + h)) - 14 (a + h) + 7$

Step 2.3

Apply the distributive property.

$6 (a \cdot a + a h + h a + h \cdot h) - 14 (a + h) + 7$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $a$ by $a$ .

$6 (a^{2} + a h + h a + h \cdot h) - 14 (a + h) + 7$

Step 3.1.2

Multiply $h$ by $h$ .

$6 (a^{2} + a h + h a + h^{2}) - 14 (a + h) + 7$

Step 3.2

Add $a h$ and $h a$ .

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Step 3.2.1

Reorder $h$ and $a$ .

$6 (a^{2} + a h + a h + h^{2}) - 14 (a + h) + 7$

Step 3.2.2

Add $a h$ and $a h$ .

$6 (a^{2} + 2 a h + h^{2}) - 14 (a + h) + 7$

Step 4

Apply the distributive property.

$6 a^{2} + 6 (2 a h) + 6 h^{2} - 14 (a + h) + 7$

Step 5

Multiply $2$ by $6$ .

$6 a^{2} + 12 (a h) + 6 h^{2} - 14 (a + h) + 7$

Step 6

Apply the distributive property.

$6 a^{2} + 12 a h + 6 h^{2} - 14 a - 14 h + 7$