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

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

Evaluate

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

Solution Steps

Multiply a+2b and a+2b to get \left(a+2b\right)^{2}.

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

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

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

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

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

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

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

Combine a^{2} and -a^{2} to get 0.

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

Combine 4ab and 2ab to get 6ab.

$$6ab+4b^{2}-b^{2}$$

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

$$6ab+3b^{2}$$

Expand

$$6ab+3b^{2}$$

Solution Steps

Multiply a+2b and a+2b to get \left(a+2b\right)^{2}.

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

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

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

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

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

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

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

Combine a^{2} and -a^{2} to get 0.

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

Combine 4ab and 2ab to get 6ab.

$$6ab+4b^{2}-b^{2}$$

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

$$6ab+3b^{2}$$