Solve (1-t^5)^3

$$( 1 - t ^ { 5 } ) ^ { 3 }$$

Expand

$$1-3t^{5}+3t^{10}-t^{15}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(1-t^{5}\right)^{3}.

$$1-3t^{5}+3\left(t^{5}\right)^{2}-\left(t^{5}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$1-3t^{5}+3t^{10}-\left(t^{5}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$1-3t^{5}+3t^{10}-t^{15}$$

Evaluate

$$\left(1-t^{5}\right)^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(1-t^{5}\right)^{3}.

$$1-3t^{5}+3\left(t^{5}\right)^{2}-\left(t^{5}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$1-3t^{5}+3t^{10}-\left(t^{5}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$1-3t^{5}+3t^{10}-t^{15}$$