Solve (x+1)(x-3)(x+1)(x+2)

$$( x + 1 ) ( x - 3 ) ( x + 1 ) ( x + 2 )$$

Evaluate

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

Solution Steps

Multiply x+1 and x+1 to get \left(x+1\right)^{2}.

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

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

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

Apply the distributive property by multiplying each term of x^{2}+2x+1 by each term of x-3.

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

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

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

Combine -6x and x to get -5x.

$$\left(x^{3}-x^{2}-5x-3\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of x^{3}-x^{2}-5x-3 by each term of x+2.

$$x^{4}+2x^{3}-x^{3}-2x^{2}-5x^{2}-10x-3x-6$$

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

$$x^{4}+x^{3}-2x^{2}-5x^{2}-10x-3x-6$$

Combine -2x^{2} and -5x^{2} to get -7x^{2}.

$$x^{4}+x^{3}-7x^{2}-10x-3x-6$$

Combine -10x and -3x to get -13x.

$$x^{4}+x^{3}-7x^{2}-13x-6$$

Expand

$$x^{4}+x^{3}-7x^{2}-13x-6$$

Solution Steps

Multiply x+1 and x+1 to get \left(x+1\right)^{2}.

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

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

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

Apply the distributive property by multiplying each term of x^{2}+2x+1 by each term of x-3.

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

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

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

Combine -6x and x to get -5x.

$$\left(x^{3}-x^{2}-5x-3\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of x^{3}-x^{2}-5x-3 by each term of x+2.

$$x^{4}+2x^{3}-x^{3}-2x^{2}-5x^{2}-10x-3x-6$$

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

$$x^{4}+x^{3}-2x^{2}-5x^{2}-10x-3x-6$$

Combine -2x^{2} and -5x^{2} to get -7x^{2}.

$$x^{4}+x^{3}-7x^{2}-10x-3x-6$$

Combine -10x and -3x to get -13x.

$$x^{4}+x^{3}-7x^{2}-13x-6$$