Solve (1-3x^2)^3

$$( 1 - 3 x ^ { 2 } ) ^ { 3 }$$

Expand

$$1-9x^{2}+27x^{4}-27x^{6}$$

Solution Steps

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

$$1-9x^{2}+27\left(x^{2}\right)^{2}-27\left(x^{2}\right)^{3}$$

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

$$1-9x^{2}+27x^{4}-27\left(x^{2}\right)^{3}$$

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

$$1-9x^{2}+27x^{4}-27x^{6}$$

Evaluate

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

Solution Steps

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

$$1-9x^{2}+27\left(x^{2}\right)^{2}-27\left(x^{2}\right)^{3}$$

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

$$1-9x^{2}+27x^{4}-27\left(x^{2}\right)^{3}$$

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

$$1-9x^{2}+27x^{4}-27x^{6}$$