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

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

Evaluate

$$\left(a+b-3\right)\left(a+b-1\right)$$

Solution Steps

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

$$a^{2}+2ab+b^{2}-4\left(a+b\right)+3$$

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

$$a^{2}+2ab+b^{2}-4a-4b+3$$

Expand

$$a^{2}+2ab-4a+b^{2}-4b+3$$

Solution Steps

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

$$a^{2}+2ab+b^{2}-4\left(a+b\right)+3$$

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

$$a^{2}+2ab+b^{2}-4a-4b+3$$