Solve (a-b)^2-16(a+b)^2

$$( a - b ) ^ { 2 } - 16 ( a + b ) ^ { 2 }$$

Evaluate

$$\left(-5a-3b\right)\left(3a+5b\right)$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-b\right)^{2}.

$$a^{2}-2ab+b^{2}-16\left(a+b\right)^{2}$$

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+b\right)^{2}.

$$a^{2}-2ab+b^{2}-16\left(a^{2}+2ab+b^{2}\right)$$

Use the distributive property to multiply -16 by a^{2}+2ab+b^{2}.

$$a^{2}-2ab+b^{2}-16a^{2}-32ab-16b^{2}$$

Combine a^{2} and -16a^{2} to get -15a^{2}.

$$-15a^{2}-2ab+b^{2}-32ab-16b^{2}$$

Combine -2ab and -32ab to get -34ab.

$$-15a^{2}-34ab+b^{2}-16b^{2}$$

Combine b^{2} and -16b^{2} to get -15b^{2}.

$$-15a^{2}-34ab-15b^{2}$$

Expand

$$-15a^{2}-34ab-15b^{2}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-b\right)^{2}.

$$a^{2}-2ab+b^{2}-16\left(a+b\right)^{2}$$

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+b\right)^{2}.

$$a^{2}-2ab+b^{2}-16\left(a^{2}+2ab+b^{2}\right)$$

Use the distributive property to multiply -16 by a^{2}+2ab+b^{2}.

$$a^{2}-2ab+b^{2}-16a^{2}-32ab-16b^{2}$$

Combine a^{2} and -16a^{2} to get -15a^{2}.

$$-15a^{2}-2ab+b^{2}-32ab-16b^{2}$$

Combine -2ab and -32ab to get -34ab.

$$-15a^{2}-34ab+b^{2}-16b^{2}$$

Combine b^{2} and -16b^{2} to get -15b^{2}.

$$-15a^{2}-34ab-15b^{2}$$