Solve 5(m+p)^2-18(m+p)-8

$$5 ( m + p ) ^ { 2 } - 18 ( m + p ) - 8$$

Evaluate

$$\left(m+p-4\right)\left(5m+5p+2\right)$$

Solution Steps

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

$$5\left(m^{2}+2mp+p^{2}\right)-18\left(m+p\right)-8$$

Use the distributive property to multiply 5 by m^{2}+2mp+p^{2}.

$$5m^{2}+10mp+5p^{2}-18\left(m+p\right)-8$$

Use the distributive property to multiply -18 by m+p.

$$5m^{2}+10mp+5p^{2}-18m-18p-8$$

Expand

$$5m^{2}+10mp-18m+5p^{2}-18p-8$$

Solution Steps

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

$$5\left(m^{2}+2mp+p^{2}\right)-18\left(m+p\right)-8$$

Use the distributive property to multiply 5 by m^{2}+2mp+p^{2}.

$$5m^{2}+10mp+5p^{2}-18\left(m+p\right)-8$$

Use the distributive property to multiply -18 by m+p.

$$5m^{2}+10mp+5p^{2}-18m-18p-8$$