Solve (a+b)^2-(4a-5b)

$$( a + b ) ^ { 2 } - ( 4 a - 5 b )$$

Evaluate

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

Solution Steps

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

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

To find the opposite of 4a-5b, find the opposite of each term.

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

Expand

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

Solution Steps

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

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

To find the opposite of 4a-5b, find the opposite of each term.

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