Solve a^2-4(a+3b)^2=

$$a ^ { 2 } - 4 ( a + 3 b ) ^ { 2 } =$$

Evaluate

$$-3\left(a+2b\right)\left(a+6b\right)$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+3b\right)^{2}.

$$a^{2}-4\left(a^{2}+6ab+9b^{2}\right)$$

Use the distributive property to multiply -4 by a^{2}+6ab+9b^{2}.

$$a^{2}-4a^{2}-24ab-36b^{2}$$

Combine a^{2} and -4a^{2} to get -3a^{2}.

$$-3a^{2}-24ab-36b^{2}$$

Expand

$$-3a^{2}-24ab-36b^{2}$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+3b\right)^{2}.

$$a^{2}-4\left(a^{2}+6ab+9b^{2}\right)$$

Use the distributive property to multiply -4 by a^{2}+6ab+9b^{2}.

$$a^{2}-4a^{2}-24ab-36b^{2}$$

Combine a^{2} and -4a^{2} to get -3a^{2}.

$$-3a^{2}-24ab-36b^{2}$$