Finite Math Examples

$(3 x + 3 h (5 - 2 x)) - 3 x (5 - 2 x + h)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 x + 3 h \cdot 5 + 3 h (- 2 x) - 3 x (5 - 2 x + h)$

Step 1.2

Multiply $5$ by $3$ .

$3 x + 15 h + 3 h (- 2 x) - 3 x (5 - 2 x + h)$

Step 1.3

Rewrite using the commutative property of multiplication.

$3 x + 15 h + 3 \cdot - 2 h x - 3 x (5 - 2 x + h)$

Step 1.4

Multiply $3$ by $- 2$ .

$3 x + 15 h - 6 h x - 3 x (5 - 2 x + h)$

Step 1.5

Apply the distributive property.

$3 x + 15 h - 6 h x - 3 x \cdot 5 - 3 x (- 2 x) - 3 x h$

Step 1.6

Simplify.

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Step 1.6.1

Multiply $5$ by $- 3$ .

$3 x + 15 h - 6 h x - 15 x - 3 x (- 2 x) - 3 x h$

Step 1.6.2

Rewrite using the commutative property of multiplication.

$3 x + 15 h - 6 h x - 15 x - 3 \cdot - 2 x \cdot x - 3 x h$

Step 1.7

Simplify each term.

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Step 1.7.1

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

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Step 1.7.1.1

Move $x$ .

$3 x + 15 h - 6 h x - 15 x - 3 \cdot - 2 (x \cdot x) - 3 x h$

Step 1.7.1.2

Multiply $x$ by $x$ .

$3 x + 15 h - 6 h x - 15 x - 3 \cdot - 2 x^{2} - 3 x h$

Step 1.7.2

Multiply $- 3$ by $- 2$ .

$3 x + 15 h - 6 h x - 15 x + 6 x^{2} - 3 x h$

Step 2

Subtract $15 x$ from $3 x$ .

$15 h - 6 h x - 12 x + 6 x^{2} - 3 x h$

Step 3

Subtract $3 x h$ from $- 6 h x$ .

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Step 3.1

Move $x$ .

$15 h - 6 h x - 3 h x - 12 x + 6 x^{2}$

Step 3.2

Subtract $3 h x$ from $- 6 h x$ .

$15 h - 9 h x - 12 x + 6 x^{2}$

Step 4

Move $- 12 x$ .

$15 h - 9 h x + 6 x^{2} - 12 x$

Step 5

Move $15 h$ .

$- 9 h x + 6 x^{2} + 15 h - 12 x$