Solve left(x-6x^3right)^2

$${ \left(x-6 { x }^{ 3 } \right) }^{ 2 }$$

Expand

$$36x^{6}-12x^{4}+x^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6x^{3}\right)^{2}.

$$x^{2}-12xx^{3}+36\left(x^{3}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$x^{2}-12x^{4}+36\left(x^{3}\right)^{2}$$

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

$$x^{2}-12x^{4}+36x^{6}$$

Evaluate

$$\left(x-6x^{3}\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6x^{3}\right)^{2}.

$$x^{2}-12xx^{3}+36\left(x^{3}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$x^{2}-12x^{4}+36\left(x^{3}\right)^{2}$$

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

$$x^{2}-12x^{4}+36x^{6}$$