Solve f(t)=3(1+t)^3

$$f ( t ) = 3 ( 1 + t ) ^ { 3 }$$

Evaluate

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

Solution Steps

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

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

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

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

Expand

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

Solution Steps

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

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

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

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