Solve (x+1)(x+1)-(x+1)(x-k)

$$( x + 1 ) ( x + 1 ) - ( x + 1 ) ( x - k )$$

Evaluate

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

Solution Steps

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

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

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

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

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

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

To find the opposite of x^{2}-xk+x-k, find the opposite of each term.

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

The opposite of -xk is xk.

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

The opposite of -k is k.

$$x^{2}+2x+1-x^{2}+xk-x+k$$

Combine x^{2} and -x^{2} to get 0.

$$2x+1+xk-x+k$$

Combine 2x and -x to get x.

$$x+1+xk+k$$

Expand

$$kx+x+k+1$$

Solution Steps

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

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

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

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

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

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

To find the opposite of x^{2}-xk+x-k, find the opposite of each term.

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

The opposite of -xk is xk.

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

The opposite of -k is k.

$$x^{2}+2x+1-x^{2}+xk-x+k$$

Combine x^{2} and -x^{2} to get 0.

$$2x+1+xk-x+k$$

Combine 2x and -x to get x.

$$x+1+xk+k$$