Solve 3left(x-3right)^2+15(x-3)+27

$$3 { \left(x-3 \right) }^{ 2 } +15(x-3)+27$$

Evaluate

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

Solution Steps

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

$$3\left(x^{2}-6x+9\right)+15\left(x-3\right)+27$$

Use the distributive property to multiply 3 by x^{2}-6x+9.

$$3x^{2}-18x+27+15\left(x-3\right)+27$$

Use the distributive property to multiply 15 by x-3.

$$3x^{2}-18x+27+15x-45+27$$

Combine -18x and 15x to get -3x.

$$3x^{2}-3x+27-45+27$$

Subtract 45 from 27 to get -18.

$$3x^{2}-3x-18+27$$

Add -18 and 27 to get 9.

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

Expand

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

Solution Steps

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

$$3\left(x^{2}-6x+9\right)+15\left(x-3\right)+27$$

Use the distributive property to multiply 3 by x^{2}-6x+9.

$$3x^{2}-18x+27+15\left(x-3\right)+27$$

Use the distributive property to multiply 15 by x-3.

$$3x^{2}-18x+27+15x-45+27$$

Combine -18x and 15x to get -3x.

$$3x^{2}-3x+27-45+27$$

Subtract 45 from 27 to get -18.

$$3x^{2}-3x-18+27$$

Add -18 and 27 to get 9.

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