Finite Math Examples

$7 x^{3} - 6 x^{2} \cdot (6 x) + (4 x^{3} + 8 x^{2} - 14 x)$

Step 1

Remove parentheses.

$7 x^{3} - 6 x^{2} \cdot (6 x) + 4 x^{3} + 8 x^{2} - 14 x$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$7 x^{3} - 6 \cdot 6 x^{2} x + 4 x^{3} + 8 x^{2} - 14 x$

Step 2.2

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 2.2.1

Move $x$ .

$7 x^{3} - 6 \cdot 6 (x \cdot x^{2}) + 4 x^{3} + 8 x^{2} - 14 x$

Step 2.2.2

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

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Step 2.2.2.1

Raise $x$ to the power of $1$ .

$7 x^{3} - 6 \cdot 6 (x^{1} x^{2}) + 4 x^{3} + 8 x^{2} - 14 x$

Step 2.2.2.2

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

$7 x^{3} - 6 \cdot 6 x^{1 + 2} + 4 x^{3} + 8 x^{2} - 14 x$

Step 2.2.3

Add $1$ and $2$ .

$7 x^{3} - 6 \cdot 6 x^{3} + 4 x^{3} + 8 x^{2} - 14 x$

Step 2.3

Multiply $- 6$ by $6$ .

$7 x^{3} - 36 x^{3} + 4 x^{3} + 8 x^{2} - 14 x$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $36 x^{3}$ from $7 x^{3}$ .

$- 29 x^{3} + 4 x^{3} + 8 x^{2} - 14 x$

Step 3.2

Add $- 29 x^{3}$ and $4 x^{3}$ .

$- 25 x^{3} + 8 x^{2} - 14 x$