Calculus Examples

${(2 x + 2 h)}^{2} - 3 x - 3 h$

Step 1

Simplify each term.

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Step 1.1

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

$(2 x + 2 h) (2 x + 2 h) - 3 x - 3 h$

Step 1.2

Expand $(2 x + 2 h) (2 x + 2 h)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$2 x (2 x + 2 h) + 2 h (2 x + 2 h) - 3 x - 3 h$

Step 1.2.2

Apply the distributive property.

$2 x (2 x) + 2 x (2 h) + 2 h (2 x + 2 h) - 3 x - 3 h$

Step 1.2.3

Apply the distributive property.

$2 x (2 x) + 2 x (2 h) + 2 h (2 x) + 2 h (2 h) - 3 x - 3 h$

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

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x (2 h) + 2 h (2 x) + 2 h (2 h) - 3 x - 3 h$

Step 1.3.1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 1.3.1.2.1

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x (2 h) + 2 h (2 x) + 2 h (2 h) - 3 x - 3 h$

Step 1.3.1.2.2

Multiply $x$ by $x$ .

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

Step 1.3.1.3

Multiply $2$ by $2$ .

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

Step 1.3.1.4

Rewrite using the commutative property of multiplication.

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

Step 1.3.1.5

Multiply $2$ by $2$ .

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

Step 1.3.1.6

Rewrite using the commutative property of multiplication.

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

Step 1.3.1.7

Multiply $2$ by $2$ .

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

Step 1.3.1.8

Rewrite using the commutative property of multiplication.

$4 x^{2} + 4 x h + 4 h x + 2 \cdot 2 h \cdot h - 3 x - 3 h$

Step 1.3.1.9

Multiply $h$ by $h$ by adding the exponents.

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Step 1.3.1.9.1

Move $h$ .

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

Step 1.3.1.9.2

Multiply $h$ by $h$ .

$4 x^{2} + 4 x h + 4 h x + 2 \cdot 2 h^{2} - 3 x - 3 h$

Step 1.3.1.10

Multiply $2$ by $2$ .

$4 x^{2} + 4 x h + 4 h x + 4 h^{2} - 3 x - 3 h$

Step 1.3.2

Add $4 x h$ and $4 h x$ .

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Step 1.3.2.1

Move $x$ .

$4 x^{2} + 4 h x + 4 h x + 4 h^{2} - 3 x - 3 h$

Step 1.3.2.2

Add $4 h x$ and $4 h x$ .

$4 x^{2} + 8 h x + 4 h^{2} - 3 x - 3 h$

Step 2

Simplify the expression.

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Step 2.1

Move $- 3 x$ .

$4 x^{2} + 8 h x + 4 h^{2} - 3 h - 3 x$

Step 2.2

Move $4 x^{2}$ .

$8 h x + 4 h^{2} + 4 x^{2} - 3 h - 3 x$

Step 2.3

Reorder $8 h x$ and $4 h^{2}$ .

$4 h^{2} + 8 h x + 4 x^{2} - 3 h - 3 x$