Solve (a+2b)^2-(a+5b)(a-b)

$$( a + 2 b ) ^ { 2 } - ( a + 5 b ) ( a - b )$$

Evaluate

$$9b^{2}$$

Solution Steps

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

$$a^{2}+4ab+4b^{2}-\left(a+5b\right)\left(a-b\right)$$

Use the distributive property to multiply a+5b by a-b and combine like terms.

$$a^{2}+4ab+4b^{2}-\left(a^{2}+4ab-5b^{2}\right)$$

To find the opposite of a^{2}+4ab-5b^{2}, find the opposite of each term.

$$a^{2}+4ab+4b^{2}-a^{2}-4ab+5b^{2}$$

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

$$4ab+4b^{2}-4ab+5b^{2}$$

Combine 4ab and -4ab to get 0.

$$4b^{2}+5b^{2}$$

Combine 4b^{2} and 5b^{2} to get 9b^{2}.

$$9b^{2}$$

Expand

$$9b^{2}$$

Solution Steps

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

$$a^{2}+4ab+4b^{2}-\left(a+5b\right)\left(a-b\right)$$

Use the distributive property to multiply a+5b by a-b and combine like terms.

$$a^{2}+4ab+4b^{2}-\left(a^{2}+4ab-5b^{2}\right)$$

To find the opposite of a^{2}+4ab-5b^{2}, find the opposite of each term.

$$a^{2}+4ab+4b^{2}-a^{2}-4ab+5b^{2}$$

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

$$4ab+4b^{2}-4ab+5b^{2}$$

Combine 4ab and -4ab to get 0.

$$4b^{2}+5b^{2}$$

Combine 4b^{2} and 5b^{2} to get 9b^{2}.

$$9b^{2}$$