Solve f(t)=(2-3t^2)^3

$$f ( t ) = ( 2 - 3 t ^ { 2 } ) ^ { 3 }$$

Evaluate

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

Solution Steps

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

$$8-36t^{2}+54\left(t^{2}\right)^{2}-27\left(t^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$8-36t^{2}+54t^{4}-27\left(t^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$8-36t^{2}+54t^{4}-27t^{6}$$

Expand

$$8-36t^{2}+54t^{4}-27t^{6}$$

Solution Steps

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

$$8-36t^{2}+54\left(t^{2}\right)^{2}-27\left(t^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$8-36t^{2}+54t^{4}-27\left(t^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$8-36t^{2}+54t^{4}-27t^{6}$$