Solve e(x)=left(2x+1right)^2-(2x+1)(-x+7)

$$e(x)= { \left(2x+1 \right) }^{ 2 } -(2x+1)(-x+7)$$

Evaluate

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

Solution Steps

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

$$4x^{2}+4x+1-\left(2x+1\right)\left(-x+7\right)$$

Use the distributive property to multiply 2x+1 by -x+7.

$$4x^{2}+4x+1-\left(2x\left(-x\right)+14x-x+7\right)$$

To find the opposite of 2x\left(-x\right)+14x-x+7, find the opposite of each term.

$$4x^{2}+4x+1-2x\left(-x\right)-14x-\left(-x\right)-7$$

Multiply -2 and -1 to get 2.

$$4x^{2}+4x+1+2xx-14x-\left(-x\right)-7$$

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

$$4x^{2}+4x+1+2x^{2}-14x-\left(-x\right)-7$$

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$6x^{2}+4x+1-14x-\left(-x\right)-7$$

Combine 4x and -14x to get -10x.

$$6x^{2}-10x+1-\left(-x\right)-7$$

Subtract 7 from 1 to get -6.

$$6x^{2}-10x-6-\left(-x\right)$$

Multiply -1 and -1 to get 1.

$$6x^{2}-10x-6+x$$

Combine -10x and x to get -9x.

$$6x^{2}-9x-6$$

Expand

$$6x^{2}-9x-6$$

Solution Steps

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

$$4x^{2}+4x+1-\left(2x+1\right)\left(-x+7\right)$$

Use the distributive property to multiply 2x+1 by -x+7.

$$4x^{2}+4x+1-\left(2x\left(-x\right)+14x-x+7\right)$$

To find the opposite of 2x\left(-x\right)+14x-x+7, find the opposite of each term.

$$4x^{2}+4x+1-2x\left(-x\right)-14x-\left(-x\right)-7$$

Multiply -2 and -1 to get 2.

$$4x^{2}+4x+1+2xx-14x-\left(-x\right)-7$$

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

$$4x^{2}+4x+1+2x^{2}-14x-\left(-x\right)-7$$

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$6x^{2}+4x+1-14x-\left(-x\right)-7$$

Combine 4x and -14x to get -10x.

$$6x^{2}-10x+1-\left(-x\right)-7$$

Subtract 7 from 1 to get -6.

$$6x^{2}-10x-6-\left(-x\right)$$

Multiply -1 and -1 to get 1.

$$6x^{2}-10x-6+x$$

Combine -10x and x to get -9x.

$$6x^{2}-9x-6$$