Simplify (x^3-10)(x^6+10x^3+100)

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

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.

Simplify each term.

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

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

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

Add $3$ and $6$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x^{3}$ .

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

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

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

Add $3$ and $3$ .

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

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

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

Multiply $10$ by $- 10$ .

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

Multiply $- 10$ by $100$ .

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

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

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

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

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

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

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

$x^{9} + 0 - 1000$

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

$x^{9} - 1000$