Solve left(1-x^2right)^3

$${ \left(1- { x }^{ 2 } \right) }^{ 3 }$$

Expand

$$1-3x^{2}+3x^{4}-x^{6}$$

Solution Steps

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

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

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

$$1-3x^{2}+3x^{4}-\left(x^{2}\right)^{3}$$

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

$$1-3x^{2}+3x^{4}-x^{6}$$

Evaluate

$$\left(1-x^{2}\right)^{3}$$

Solution Steps

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

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

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

$$1-3x^{2}+3x^{4}-\left(x^{2}\right)^{3}$$

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

$$1-3x^{2}+3x^{4}-x^{6}$$