Simplify (8n^2+3n^7)(8n^2-3n^7)

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

Step 1

Expand $(8 n^{2} + 3 n^{7}) (8 n^{2} - 3 n^{7})$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

Combine the opposite terms in $8 n^{2} (8 n^{2}) + 8 n^{2} (- 3 n^{7}) + 3 n^{7} (8 n^{2}) + 3 n^{7} (- 3 n^{7})$ .

Reorder the factors in the terms $8 n^{2} (- 3 n^{7})$ and $3 n^{7} (8 n^{2})$ .

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

Add $- 3 \cdot 8 n^{7} n^{2}$ and $3 \cdot 8 n^{7} n^{2}$ .

$8 n^{2} (8 n^{2}) + 0 + 3 n^{7} (- 3 n^{7})$

Add $8 n^{2} (8 n^{2})$ and $0$ .

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

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $n^{2}$ .

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

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

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

Add $2$ and $2$ .

$8 \cdot 8 n^{4} + 3 n^{7} (- 3 n^{7})$

Multiply $8$ by $8$ .

$64 n^{4} + 3 n^{7} (- 3 n^{7})$

Rewrite using the commutative property of multiplication.

$64 n^{4} + 3 \cdot - 3 n^{7} n^{7}$

Multiply $n^{7}$ by $n^{7}$ by adding the exponents.

Move $n^{7}$ .

$64 n^{4} + 3 \cdot - 3 (n^{7} n^{7})$

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

$64 n^{4} + 3 \cdot - 3 n^{7 + 7}$

Add $7$ and $7$ .

$64 n^{4} + 3 \cdot - 3 n^{14}$

Multiply $3$ by $- 3$ .

$64 n^{4} - 9 n^{14}$