Solve (4a+6b)^2-16(4a+6b)+64

$$( 4 a + 6 b ) ^ { 2 } - 16 ( 4 a + 6 b ) + 64$$

Evaluate

$$4\left(2a+3b-4\right)^{2}$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(4a+6b\right)^{2}.

$$16a^{2}+48ab+36b^{2}-16\left(4a+6b\right)+64$$

Use the distributive property to multiply -16 by 4a+6b.

$$16a^{2}+48ab+36b^{2}-64a-96b+64$$

Expand

$$16a^{2}+48ab-64a+36b^{2}-96b+64$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(4a+6b\right)^{2}.

$$16a^{2}+48ab+36b^{2}-16\left(4a+6b\right)+64$$

Use the distributive property to multiply -16 by 4a+6b.

$$16a^{2}+48ab+36b^{2}-64a-96b+64$$