Solve (a+b)^2-4(a+b-1)

$$( a + b ) ^ { 2 } - 4 ( a + b - 1 )$$

Evaluate

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

Solution Steps

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

$$a^{2}+2ab+b^{2}-4\left(a+b-1\right)$$

Use the distributive property to multiply -4 by a+b-1.

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

Expand

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

Solution Steps

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

$$a^{2}+2ab+b^{2}-4\left(a+b-1\right)$$

Use the distributive property to multiply -4 by a+b-1.

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