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

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

Evaluate

$$6x+10$$

Solution Steps

To find the opposite of x+3, find the opposite of each term.

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

Combine x and -x to get 0.

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

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

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

To find the opposite of x^{2}+2x+1, find the opposite of each term.

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

Subtract 1 from -3 to get -4.

$$-4-x^{2}-2x-\left(x+2\right)^{2}+2\left(x+3\right)^{2}$$

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

$$-4-x^{2}-2x-\left(x^{2}+4x+4\right)+2\left(x+3\right)^{2}$$

To find the opposite of x^{2}+4x+4, find the opposite of each term.

$$-4-x^{2}-2x-x^{2}-4x-4+2\left(x+3\right)^{2}$$

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

$$-4-2x^{2}-2x-4x-4+2\left(x+3\right)^{2}$$

Combine -2x and -4x to get -6x.

$$-4-2x^{2}-6x-4+2\left(x+3\right)^{2}$$

Subtract 4 from -4 to get -8.

$$-8-2x^{2}-6x+2\left(x+3\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.

$$-8-2x^{2}-6x+2\left(x^{2}+6x+9\right)$$

Use the distributive property to multiply 2 by x^{2}+6x+9.

$$-8-2x^{2}-6x+2x^{2}+12x+18$$

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

$$-8-6x+12x+18$$

Combine -6x and 12x to get 6x.

$$-8+6x+18$$

Add -8 and 18 to get 10.

$$10+6x$$

Expand

$$6x+10$$

Solution Steps

To find the opposite of x+3, find the opposite of each term.

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

Combine x and -x to get 0.

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

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

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

To find the opposite of x^{2}+2x+1, find the opposite of each term.

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

Subtract 1 from -3 to get -4.

$$-4-x^{2}-2x-\left(x+2\right)^{2}+2\left(x+3\right)^{2}$$

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

$$-4-x^{2}-2x-\left(x^{2}+4x+4\right)+2\left(x+3\right)^{2}$$

To find the opposite of x^{2}+4x+4, find the opposite of each term.

$$-4-x^{2}-2x-x^{2}-4x-4+2\left(x+3\right)^{2}$$

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

$$-4-2x^{2}-2x-4x-4+2\left(x+3\right)^{2}$$

Combine -2x and -4x to get -6x.

$$-4-2x^{2}-6x-4+2\left(x+3\right)^{2}$$

Subtract 4 from -4 to get -8.

$$-8-2x^{2}-6x+2\left(x+3\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.

$$-8-2x^{2}-6x+2\left(x^{2}+6x+9\right)$$

Use the distributive property to multiply 2 by x^{2}+6x+9.

$$-8-2x^{2}-6x+2x^{2}+12x+18$$

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

$$-8-6x+12x+18$$

Combine -6x and 12x to get 6x.

$$-8+6x+18$$

Add -8 and 18 to get 10.

$$10+6x$$