Solve (h+k)^2-5(h+k)+6

$$( h + k ) ^ { 2 } - 5 ( h + k ) + 6$$

Evaluate

$$\left(h+k-3\right)\left(h+k-2\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(h+k\right)^{2}.

$$h^{2}+2hk+k^{2}-5\left(h+k\right)+6$$

Use the distributive property to multiply -5 by h+k.

$$h^{2}+2hk+k^{2}-5h-5k+6$$

Expand

$$h^{2}+2hk-5h+k^{2}-5k+6$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(h+k\right)^{2}.

$$h^{2}+2hk+k^{2}-5\left(h+k\right)+6$$

Use the distributive property to multiply -5 by h+k.

$$h^{2}+2hk+k^{2}-5h-5k+6$$