Solve 2(x+1)+left(x-3right)^2-3left(x+1right)^2(x-3)

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

Evaluate

$$20+11x+4x^{2}-3x^{3}$$

Solution Steps

Use the distributive property to multiply 2 by x+1.

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

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

$$2x+2+x^{2}-6x+9-3\left(x+1\right)^{2}\left(x-3\right)$$

Combine 2x and -6x to get -4x.

$$-4x+2+x^{2}+9-3\left(x+1\right)^{2}\left(x-3\right)$$

Add 2 and 9 to get 11.

$$-4x+11+x^{2}-3\left(x+1\right)^{2}\left(x-3\right)$$

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

$$-4x+11+x^{2}-3\left(x^{2}+2x+1\right)\left(x-3\right)$$

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

$$-4x+11+x^{2}+\left(-3x^{2}-6x-3\right)\left(x-3\right)$$

Use the distributive property to multiply -3x^{2}-6x-3 by x-3 and combine like terms.

$$-4x+11+x^{2}-3x^{3}+3x^{2}+15x+9$$

Combine x^{2} and 3x^{2} to get 4x^{2}.

$$-4x+11+4x^{2}-3x^{3}+15x+9$$

Combine -4x and 15x to get 11x.

$$11x+11+4x^{2}-3x^{3}+9$$

Add 11 and 9 to get 20.

$$11x+20+4x^{2}-3x^{3}$$

Expand

$$20+11x+4x^{2}-3x^{3}$$

Solution Steps

Use the distributive property to multiply 2 by x+1.

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

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

$$2x+2+x^{2}-6x+9-3\left(x+1\right)^{2}\left(x-3\right)$$

Combine 2x and -6x to get -4x.

$$-4x+2+x^{2}+9-3\left(x+1\right)^{2}\left(x-3\right)$$

Add 2 and 9 to get 11.

$$-4x+11+x^{2}-3\left(x+1\right)^{2}\left(x-3\right)$$

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

$$-4x+11+x^{2}-3\left(x^{2}+2x+1\right)\left(x-3\right)$$

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

$$-4x+11+x^{2}+\left(-3x^{2}-6x-3\right)\left(x-3\right)$$

Use the distributive property to multiply -3x^{2}-6x-3 by x-3 and combine like terms.

$$-4x+11+x^{2}-3x^{3}+3x^{2}+15x+9$$

Combine x^{2} and 3x^{2} to get 4x^{2}.

$$-4x+11+4x^{2}-3x^{3}+15x+9$$

Combine -4x and 15x to get 11x.

$$11x+11+4x^{2}-3x^{3}+9$$

Add 11 and 9 to get 20.

$$11x+20+4x^{2}-3x^{3}$$