Solve =3(c+h)^2-5(c+h)+7

$$= 3 ( c + h ) ^ { 2 } - 5 ( c + h ) + 7$$

Evaluate

$$3\left(c+h\right)^{2}-5c-5h+7$$

Solution Steps

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

$$3\left(c^{2}+2ch+h^{2}\right)-5\left(c+h\right)+7$$

Use the distributive property to multiply 3 by c^{2}+2ch+h^{2}.

$$3c^{2}+6ch+3h^{2}-5\left(c+h\right)+7$$

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

$$3c^{2}+6ch+3h^{2}-5c-5h+7$$

Expand

$$3c^{2}+6ch-5c+3h^{2}-5h+7$$

Solution Steps

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

$$3\left(c^{2}+2ch+h^{2}\right)-5\left(c+h\right)+7$$

Use the distributive property to multiply 3 by c^{2}+2ch+h^{2}.

$$3c^{2}+6ch+3h^{2}-5\left(c+h\right)+7$$

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

$$3c^{2}+6ch+3h^{2}-5c-5h+7$$