Algebra Examples

$(3 x^{3}) (2 x^{2} - 7 x - 8) x^{3}$

Step 1

Multiply $x^{3}$ by $x^{3}$ by adding the exponents.

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Step 1.1

Move $x^{3}$ .

$3 (x^{3} x^{3}) (2 x^{2} - 7 x - 8)$

Step 1.2

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

$3 x^{3 + 3} (2 x^{2} - 7 x - 8)$

Step 1.3

Add $3$ and $3$ .

$3 x^{6} (2 x^{2} - 7 x - 8)$

Step 2

Apply the distributive property.

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

Step 3

Simplify.

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Step 3.1

Rewrite using the commutative property of multiplication.

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

Step 3.2

Rewrite using the commutative property of multiplication.

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

Step 3.3

Multiply $- 8$ by $3$ .

$3 \cdot 2 x^{6} x^{2} + 3 \cdot - 7 x^{6} x - 24 x^{6}$

Step 4

Simplify each term.

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Step 4.1

Multiply $x^{6}$ by $x^{2}$ by adding the exponents.

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Step 4.1.1

Move $x^{2}$ .

$3 \cdot 2 (x^{2} x^{6}) + 3 \cdot - 7 x^{6} x - 24 x^{6}$

Step 4.1.2

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

$3 \cdot 2 x^{2 + 6} + 3 \cdot - 7 x^{6} x - 24 x^{6}$

Step 4.1.3

Add $2$ and $6$ .

$3 \cdot 2 x^{8} + 3 \cdot - 7 x^{6} x - 24 x^{6}$

Step 4.2

Multiply $3$ by $2$ .

$6 x^{8} + 3 \cdot - 7 x^{6} x - 24 x^{6}$

Step 4.3

Multiply $x^{6}$ by $x$ by adding the exponents.

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Step 4.3.1

Move $x$ .

$6 x^{8} + 3 \cdot - 7 (x \cdot x^{6}) - 24 x^{6}$

Step 4.3.2

Multiply $x$ by $x^{6}$ .

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Step 4.3.2.1

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

$6 x^{8} + 3 \cdot - 7 (x^{1} x^{6}) - 24 x^{6}$

Step 4.3.2.2

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

$6 x^{8} + 3 \cdot - 7 x^{1 + 6} - 24 x^{6}$

Step 4.3.3

Add $1$ and $6$ .

$6 x^{8} + 3 \cdot - 7 x^{7} - 24 x^{6}$

Step 4.4

Multiply $3$ by $- 7$ .

$6 x^{8} - 21 x^{7} - 24 x^{6}$