Calculus Examples

$8 {(5 + h)}^{2} + 7 (5 + h) + 6$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(5 + h)}^{2}$ as $(5 + h) (5 + h)$ .

$8 ((5 + h) (5 + h)) + 7 (5 + h) + 6$

Step 1.2

Expand $(5 + h) (5 + h)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$8 (5 (5 + h) + h (5 + h)) + 7 (5 + h) + 6$

Step 1.2.2

Apply the distributive property.

$8 (5 \cdot 5 + 5 h + h (5 + h)) + 7 (5 + h) + 6$

Step 1.2.3

Apply the distributive property.

$8 (5 \cdot 5 + 5 h + h \cdot 5 + h \cdot h) + 7 (5 + h) + 6$

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 $5$ by $5$ .

$8 (25 + 5 h + h \cdot 5 + h \cdot h) + 7 (5 + h) + 6$

Step 1.3.1.2

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

$8 (25 + 5 h + 5 \cdot h + h \cdot h) + 7 (5 + h) + 6$

Step 1.3.1.3

Multiply $h$ by $h$ .

$8 (25 + 5 h + 5 h + h^{2}) + 7 (5 + h) + 6$

Step 1.3.2

Add $5 h$ and $5 h$ .

$8 (25 + 10 h + h^{2}) + 7 (5 + h) + 6$

Step 1.4

Apply the distributive property.

$8 \cdot 25 + 8 (10 h) + 8 h^{2} + 7 (5 + h) + 6$

Step 1.5

Simplify.

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Step 1.5.1

Multiply $8$ by $25$ .

$200 + 8 (10 h) + 8 h^{2} + 7 (5 + h) + 6$

Step 1.5.2

Multiply $10$ by $8$ .

$200 + 80 h + 8 h^{2} + 7 (5 + h) + 6$

Step 1.6

Apply the distributive property.

$200 + 80 h + 8 h^{2} + 7 \cdot 5 + 7 h + 6$

Step 1.7

Multiply $7$ by $5$ .

$200 + 80 h + 8 h^{2} + 35 + 7 h + 6$

Step 2

Simplify by adding terms.

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Step 2.1

Add $200$ and $35$ .

$80 h + 8 h^{2} + 235 + 7 h + 6$

Step 2.2

Add $80 h$ and $7 h$ .

$87 h + 8 h^{2} + 235 + 6$

Step 2.3

Simplify the expression.

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Step 2.3.1

Add $235$ and $6$ .

$87 h + 8 h^{2} + 241$

Step 2.3.2

Reorder $87 h$ and $8 h^{2}$ .

$8 h^{2} + 87 h + 241$