Solve 3(1+h)^3

$$3 ( 1 + h ) ^ { 3 }$$

Evaluate

$$3\left(h+1\right)^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(1+h\right)^{3}.

$$3\left(1+3h+3h^{2}+h^{3}\right)$$

Use the distributive property to multiply 3 by 1+3h+3h^{2}+h^{3}.

$$3+9h+9h^{2}+3h^{3}$$

Expand

$$3h^{3}+9h^{2}+9h+3$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(1+h\right)^{3}.

$$3\left(1+3h+3h^{2}+h^{3}\right)$$

Use the distributive property to multiply 3 by 1+3h+3h^{2}+h^{3}.

$$3+9h+9h^{2}+3h^{3}$$