Finite Math Examples

$(x^{2} + x - 12) \cdot (x^{2} - 4)$

Multiply $x^{2} + x - 12$ by $x^{2} - 4$ .

$(x^{2} + x - 12) (x^{2} - 4)$

Expand $(x^{2} + x - 12) (x^{2} - 4)$ by multiplying each term in the first expression by each term in the second expression.

$x^{2} x^{2} + x^{2} \cdot - 4 + (x x^{2} + x \cdot - 4) + (- 12 x^{2} - 12 \cdot - 4)$

Simplify terms.

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Remove unnecessary parentheses.

$x^{2} x^{2} + x^{2} \cdot - 4 + x x^{2} + x \cdot - 4 - 12 x^{2} - 12 \cdot - 4$

Simplify each term.

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Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2 + 2} + x^{2} \cdot - 4 + x x^{2} + x \cdot - 4 - 12 x^{2} - 12 \cdot - 4$

Add $2$ and $2$ .

$x^{4} + x^{2} \cdot - 4 + x x^{2} + x \cdot - 4 - 12 x^{2} - 12 \cdot - 4$

Move $- 4$ to the left of the expression $x^{2} \cdot - 4$ .

$x^{4} - 4 \cdot x^{2} + x x^{2} + x \cdot - 4 - 12 x^{2} - 12 \cdot - 4$

Multiply $- 4$ by $x^{2}$ .

$x^{4} - 4 x^{2} + x x^{2} + x \cdot - 4 - 12 x^{2} - 12 \cdot - 4$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{4} - 4 x^{2} + x^{1 + 2} + x \cdot - 4 - 12 x^{2} - 12 \cdot - 4$

Add $1$ and $2$ .

$x^{4} - 4 x^{2} + x^{3} + x \cdot - 4 - 12 x^{2} - 12 \cdot - 4$

Move $- 4$ to the left of the expression $x \cdot - 4$ .

$x^{4} - 4 x^{2} + x^{3} - 4 \cdot x - 12 x^{2} - 12 \cdot - 4$

Multiply $- 4$ by $x$ .

$x^{4} - 4 x^{2} + x^{3} - 4 x - 12 x^{2} - 12 \cdot - 4$

Multiply $- 12$ by $- 4$ .

$x^{4} - 4 x^{2} + x^{3} - 4 x - 12 x^{2} + 48$

Simplify by adding terms.

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Subtract $12 x^{2}$ from $- 4 x^{2}$ .

$x^{4} - 16 x^{2} + x^{3} - 4 x + 48$

Move $- 16 x^{2}$ .

$x^{4} + x^{3} - 16 x^{2} - 4 x + 48$

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