Simplify (8rs^2-6)^2

${(8 r s^{2} - 6)}^{2}$

Rewrite ${(8 r s^{2} - 6)}^{2}$ as $(8 r s^{2} - 6) (8 r s^{2} - 6)$ .

$(8 r s^{2} - 6) (8 r s^{2} - 6)$

Expand $(8 r s^{2} - 6) (8 r s^{2} - 6)$ using the FOIL Method.

Apply the distributive property.

$8 r s^{2} (8 r s^{2} - 6) - 6 (8 r s^{2} - 6)$

Apply the distributive property.

$8 r s^{2} (8 r s^{2}) + 8 r s^{2} \cdot - 6 - 6 (8 r s^{2} - 6)$

Apply the distributive property.

$8 r s^{2} (8 r s^{2}) + 8 r s^{2} \cdot - 6 - 6 (8 r s^{2}) - 6 \cdot - 6$

Simplify and combine like terms.

Simplify each term.

Multiply $r$ by $r$ by adding the exponents.

Move $r$ .

$8 (r \cdot r) s^{2} (8 s^{2}) + 8 r s^{2} \cdot - 6 - 6 (8 r s^{2}) - 6 \cdot - 6$

Multiply $r$ by $r$ .

$8 r^{2} s^{2} (8 s^{2}) + 8 r s^{2} \cdot - 6 - 6 (8 r s^{2}) - 6 \cdot - 6$

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

Move $s^{2}$ .

$8 r^{2} (s^{2} s^{2}) \cdot 8 + 8 r s^{2} \cdot - 6 - 6 (8 r s^{2}) - 6 \cdot - 6$

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

$8 r^{2} s^{2 + 2} \cdot 8 + 8 r s^{2} \cdot - 6 - 6 (8 r s^{2}) - 6 \cdot - 6$

Add $2$ and $2$ .

$8 r^{2} s^{4} \cdot 8 + 8 r s^{2} \cdot - 6 - 6 (8 r s^{2}) - 6 \cdot - 6$

Multiply $8$ by $8$ .

$64 r^{2} s^{4} + 8 r s^{2} \cdot - 6 - 6 (8 r s^{2}) - 6 \cdot - 6$

Multiply $- 6$ by $8$ .

$64 r^{2} s^{4} - 48 r s^{2} - 6 (8 r s^{2}) - 6 \cdot - 6$

Multiply $8$ by $- 6$ .

$64 r^{2} s^{4} - 48 r s^{2} - 48 (r s^{2}) - 6 \cdot - 6$

Multiply $- 6$ by $- 6$ .

$64 r^{2} s^{4} - 48 r s^{2} - 48 r s^{2} + 36$

Subtract $48 r s^{2}$ from $- 48 r s^{2}$ .

$64 r^{2} s^{4} - 96 r s^{2} + 36$