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

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

Evaluate

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

Solution Steps

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

$$\left(9x^{2}-6x+1-1\right)^{2}$$

Subtract 1 from 1 to get 0.

$$\left(9x^{2}-6x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(9x^{2}-6x\right)^{2}.

$$81\left(x^{2}\right)^{2}-108x^{2}x+36x^{2}$$

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

$$81x^{4}-108x^{2}x+36x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$81x^{4}-108x^{3}+36x^{2}$$

Expand

$$81x^{4}-108x^{3}+36x^{2}$$

Solution Steps

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

$$\left(9x^{2}-6x+1-1\right)^{2}$$

Subtract 1 from 1 to get 0.

$$\left(9x^{2}-6x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(9x^{2}-6x\right)^{2}.

$$81\left(x^{2}\right)^{2}-108x^{2}x+36x^{2}$$

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

$$81x^{4}-108x^{2}x+36x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$81x^{4}-108x^{3}+36x^{2}$$