Solve (1-9x^9)^2

$$( 1 - 9 x ^ { 9 } ) ^ { 2 }$$

Expand

$$81x^{18}-18x^{9}+1$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-9x^{9}\right)^{2}.

$$1-18x^{9}+81\left(x^{9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$1-18x^{9}+81x^{18}$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-9x^{9}\right)^{2}.

$$1-18x^{9}+81\left(x^{9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$1-18x^{9}+81x^{18}$$