Solve (10x^3-9x)^2=

$$( 10 x ^ { 3 } - 9 x ) ^ { 2 } =$$

Evaluate

$$\left(x\left(10x^{2}-9\right)\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(10x^{3}-9x\right)^{2}.

$$100\left(x^{3}\right)^{2}-180x^{3}x+81x^{2}$$

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

$$100x^{6}-180x^{3}x+81x^{2}$$

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

$$100x^{6}-180x^{4}+81x^{2}$$

Expand

$$100x^{6}-180x^{4}+81x^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(10x^{3}-9x\right)^{2}.

$$100\left(x^{3}\right)^{2}-180x^{3}x+81x^{2}$$

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

$$100x^{6}-180x^{3}x+81x^{2}$$

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

$$100x^{6}-180x^{4}+81x^{2}$$