Solve left(x+4right)left(x+1right)+(x-4)(x+1)

$$\left( x+4 \right) \left( x+1 \right) +(x-4)(x+1)$$

Evaluate

$$2x\left(x+1\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x+4 by each term of x+1.

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

Combine x and 4x to get 5x.

$$x^{2}+5x+4+\left(x-4\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of x-4 by each term of x+1.

$$x^{2}+5x+4+x^{2}+x-4x-4$$

Combine x and -4x to get -3x.

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

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

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

Combine 5x and -3x to get 2x.

$$2x^{2}+2x+4-4$$

Subtract 4 from 4 to get 0.

$$2x^{2}+2x$$

Expand

$$2x^{2}+2x$$

Solution Steps

Apply the distributive property by multiplying each term of x+4 by each term of x+1.

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

Combine x and 4x to get 5x.

$$x^{2}+5x+4+\left(x-4\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of x-4 by each term of x+1.

$$x^{2}+5x+4+x^{2}+x-4x-4$$

Combine x and -4x to get -3x.

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

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

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

Combine 5x and -3x to get 2x.

$$2x^{2}+2x+4-4$$

Subtract 4 from 4 to get 0.

$$2x^{2}+2x$$