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

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

Evaluate

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

Solution Steps

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

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

Use the distributive property to multiply 2x+3 by x-1 and combine like terms.

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

To find the opposite of 2x^{2}+x-3, find the opposite of each term.

$$x^{2}+2x+1-2x^{2}-x+3$$

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

$$-x^{2}+2x+1-x+3$$

Combine 2x and -x to get x.

$$-x^{2}+x+1+3$$

Add 1 and 3 to get 4.

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

Expand

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

Solution Steps

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

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

Use the distributive property to multiply 2x+3 by x-1 and combine like terms.

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

To find the opposite of 2x^{2}+x-3, find the opposite of each term.

$$x^{2}+2x+1-2x^{2}-x+3$$

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

$$-x^{2}+2x+1-x+3$$

Combine 2x and -x to get x.

$$-x^{2}+x+1+3$$

Add 1 and 3 to get 4.

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