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

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

Evaluate

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

Solution Steps

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

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

Use the distributive property to multiply -3 by x+1.

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

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

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

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

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

Add 1 and 3 to get 4.

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

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

$$2x+4$$

Expand

$$2x+4$$

Solution Steps

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

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

Use the distributive property to multiply -3 by x+1.

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

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

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

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

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

Add 1 and 3 to get 4.

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

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

$$2x+4$$