Simplify (5x^3+2)(5x^3-2)

$(5 x^{3} + 2) (5 x^{3} - 2)$

Step 1

Expand $(5 x^{3} + 2) (5 x^{3} - 2)$ using the FOIL Method.

Apply the distributive property.

$5 x^{3} (5 x^{3} - 2) + 2 (5 x^{3} - 2)$

Apply the distributive property.

$5 x^{3} (5 x^{3}) + 5 x^{3} \cdot - 2 + 2 (5 x^{3} - 2)$

Apply the distributive property.

$5 x^{3} (5 x^{3}) + 5 x^{3} \cdot - 2 + 2 (5 x^{3}) + 2 \cdot - 2$

Step 2

Simplify terms.

Combine the opposite terms in $5 x^{3} (5 x^{3}) + 5 x^{3} \cdot - 2 + 2 (5 x^{3}) + 2 \cdot - 2$ .

Reorder the factors in the terms $5 x^{3} \cdot - 2$ and $2 (5 x^{3})$ .

$5 x^{3} (5 x^{3}) - 2 \cdot 5 x^{3} + 2 \cdot 5 x^{3} + 2 \cdot - 2$

Add $- 2 \cdot 5 x^{3}$ and $2 \cdot 5 x^{3}$ .

$5 x^{3} (5 x^{3}) + 0 + 2 \cdot - 2$

Add $5 x^{3} (5 x^{3})$ and $0$ .

$5 x^{3} (5 x^{3}) + 2 \cdot - 2$

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 x^{3} x^{3} + 2 \cdot - 2$

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

Move $x^{3}$ .

$5 \cdot 5 (x^{3} x^{3}) + 2 \cdot - 2$

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

$5 \cdot 5 x^{3 + 3} + 2 \cdot - 2$

Add $3$ and $3$ .

$5 \cdot 5 x^{6} + 2 \cdot - 2$

Multiply $5$ by $5$ .

$25 x^{6} + 2 \cdot - 2$

Multiply $2$ by $- 2$ .

$25 x^{6} - 4$