Solve 4left(x-3right)^2(x-3)

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

Evaluate

$$4\left(x-3\right)^{3}$$

Solution Steps

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

$$4\left(x-3\right)^{3}$$

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

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

Use the distributive property to multiply 4 by x^{3}-9x^{2}+27x-27.

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

Expand

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

Solution Steps

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

$$4\left(x-3\right)^{3}$$

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

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

Use the distributive property to multiply 4 by x^{3}-9x^{2}+27x-27.

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