Solve f(x)=3(x-1)^3-7

$$f ( x ) = 3 ( x - 1 ) ^ { 3 } - 7$$

Evaluate

$$3\left(x-1\right)^{3}-7$$

Solution Steps

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

$$3\left(x^{3}-3x^{2}+3x-1\right)-7$$

Use the distributive property to multiply 3 by x^{3}-3x^{2}+3x-1.

$$3x^{3}-9x^{2}+9x-3-7$$

Subtract 7 from -3 to get -10.

$$3x^{3}-9x^{2}+9x-10$$

Expand

$$3x^{3}-9x^{2}+9x-10$$

Solution Steps

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

$$3\left(x^{3}-3x^{2}+3x-1\right)-7$$

Use the distributive property to multiply 3 by x^{3}-3x^{2}+3x-1.

$$3x^{3}-9x^{2}+9x-3-7$$

Subtract 7 from -3 to get -10.

$$3x^{3}-9x^{2}+9x-10$$