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

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

Evaluate

$$7b\left(2a-b\right)$$

Solution Steps

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

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

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

$$a^{2}+6ab+9b^{2}-\left(a^{2}-8ab+16b^{2}\right)$$

To find the opposite of a^{2}-8ab+16b^{2}, find the opposite of each term.

$$a^{2}+6ab+9b^{2}-a^{2}+8ab-16b^{2}$$

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

$$6ab+9b^{2}+8ab-16b^{2}$$

Combine 6ab and 8ab to get 14ab.

$$14ab+9b^{2}-16b^{2}$$

Combine 9b^{2} and -16b^{2} to get -7b^{2}.

$$14ab-7b^{2}$$

Expand

$$14ab-7b^{2}$$

Solution Steps

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

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

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

$$a^{2}+6ab+9b^{2}-\left(a^{2}-8ab+16b^{2}\right)$$

To find the opposite of a^{2}-8ab+16b^{2}, find the opposite of each term.

$$a^{2}+6ab+9b^{2}-a^{2}+8ab-16b^{2}$$

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

$$6ab+9b^{2}+8ab-16b^{2}$$

Combine 6ab and 8ab to get 14ab.

$$14ab+9b^{2}-16b^{2}$$

Combine 9b^{2} and -16b^{2} to get -7b^{2}.

$$14ab-7b^{2}$$