Solve {l}{2a(a+2b)}{-(a+2b)^2}

$$\left. \begin{array} { l } { 2 a ( a + 2 b ) } \\ { - ( a + 2 b ) ^ { 2 } } \end{array} \right.$$

Evaluate

$$a^{2}-4b^{2}$$

Solution Steps

Use the distributive property to multiply 2a by a+2b.

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

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

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

To find the opposite of a^{2}+4ab+4b^{2}, find the opposite of each term.

$$2a^{2}+4ab-a^{2}-4ab-4b^{2}$$

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

$$a^{2}+4ab-4ab-4b^{2}$$

Combine 4ab and -4ab to get 0.

$$a^{2}-4b^{2}$$

Expand

$$a^{2}-4b^{2}$$

Solution Steps

Use the distributive property to multiply 2a by a+2b.

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

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

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

To find the opposite of a^{2}+4ab+4b^{2}, find the opposite of each term.

$$2a^{2}+4ab-a^{2}-4ab-4b^{2}$$

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

$$a^{2}+4ab-4ab-4b^{2}$$

Combine 4ab and -4ab to get 0.

$$a^{2}-4b^{2}$$