Algebra Examples

$(x^{3} - 10) (x^{6} + 10 x^{3} + 100)$

Step 1

Expand $(x^{3} - 10) (x^{6} + 10 x^{3} + 100)$ by multiplying each term in the first expression by each term in the second expression.

$x^{3} x^{6} + x^{3} (10 x^{3}) + x^{3} \cdot 100 - 10 x^{6} - 10 (10 x^{3}) - 10 \cdot 100$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $x^{3}$ by $x^{6}$ by adding the exponents.

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Step 2.1.1.1

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

$x^{3 + 6} + x^{3} (10 x^{3}) + x^{3} \cdot 100 - 10 x^{6} - 10 (10 x^{3}) - 10 \cdot 100$

Step 2.1.1.2

Add $3$ and $6$ .

$x^{9} + x^{3} (10 x^{3}) + x^{3} \cdot 100 - 10 x^{6} - 10 (10 x^{3}) - 10 \cdot 100$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$x^{9} + 10 x^{3} x^{3} + x^{3} \cdot 100 - 10 x^{6} - 10 (10 x^{3}) - 10 \cdot 100$

Step 2.1.3

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

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Step 2.1.3.1

Move $x^{3}$ .

$x^{9} + 10 (x^{3} x^{3}) + x^{3} \cdot 100 - 10 x^{6} - 10 (10 x^{3}) - 10 \cdot 100$

Step 2.1.3.2

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

$x^{9} + 10 x^{3 + 3} + x^{3} \cdot 100 - 10 x^{6} - 10 (10 x^{3}) - 10 \cdot 100$

Step 2.1.3.3

Add $3$ and $3$ .

$x^{9} + 10 x^{6} + x^{3} \cdot 100 - 10 x^{6} - 10 (10 x^{3}) - 10 \cdot 100$

Step 2.1.4

Move $100$ to the left of $x^{3}$ .

$x^{9} + 10 x^{6} + 100 \cdot x^{3} - 10 x^{6} - 10 (10 x^{3}) - 10 \cdot 100$

Step 2.1.5

Multiply $10$ by $- 10$ .

$x^{9} + 10 x^{6} + 100 x^{3} - 10 x^{6} - 100 x^{3} - 10 \cdot 100$

Step 2.1.6

Multiply $- 10$ by $100$ .

$x^{9} + 10 x^{6} + 100 x^{3} - 10 x^{6} - 100 x^{3} - 1000$

Step 2.2

Combine the opposite terms in $x^{9} + 10 x^{6} + 100 x^{3} - 10 x^{6} - 100 x^{3} - 1000$ .

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Step 2.2.1

Subtract $10 x^{6}$ from $10 x^{6}$ .

$x^{9} + 100 x^{3} + 0 - 100 x^{3} - 1000$

Step 2.2.2

Add $x^{9} + 100 x^{3}$ and $0$ .

$x^{9} + 100 x^{3} - 100 x^{3} - 1000$

Step 2.2.3

Subtract $100 x^{3}$ from $100 x^{3}$ .

$x^{9} + 0 - 1000$

Step 2.2.4

Add $x^{9}$ and $0$ .

$x^{9} - 1000$