Solve g(x)=3(3-x)^2(6x)(3-x)

$$g ( x ) = 3 ( 3 - x ) ^ { 2 } ( 6 x ) ( 3 - x )$$

Evaluate

$$18x\left(3-x\right)^{3}$$

Solution Steps

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

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

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

$$3\left(27-27x+9x^{2}-x^{3}\right)\times 6x$$

Multiply 3 and 6 to get 18.

$$18\left(27-27x+9x^{2}-x^{3}\right)x$$

Use the distributive property to multiply 18 by 27-27x+9x^{2}-x^{3}.

$$\left(486-486x+162x^{2}-18x^{3}\right)x$$

Use the distributive property to multiply 486-486x+162x^{2}-18x^{3} by x.

$$486x-486x^{2}+162x^{3}-18x^{4}$$

Expand

$$486x-486x^{2}+162x^{3}-18x^{4}$$

Solution Steps

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

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

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

$$3\left(27-27x+9x^{2}-x^{3}\right)\times 6x$$

Multiply 3 and 6 to get 18.

$$18\left(27-27x+9x^{2}-x^{3}\right)x$$

Use the distributive property to multiply 18 by 27-27x+9x^{2}-x^{3}.

$$\left(486-486x+162x^{2}-18x^{3}\right)x$$

Use the distributive property to multiply 486-486x+162x^{2}-18x^{3} by x.

$$486x-486x^{2}+162x^{3}-18x^{4}$$