Solve left(4x+2right)^2-(x+1)(4x+2)

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

Evaluate

$$12x^{2}+10x+2$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4x+2\right)^{2}.

$$16x^{2}+16x+4-\left(x+1\right)\left(4x+2\right)$$

Use the distributive property to multiply x+1 by 4x+2 and combine like terms.

$$16x^{2}+16x+4-\left(4x^{2}+6x+2\right)$$

To find the opposite of 4x^{2}+6x+2, find the opposite of each term.

$$16x^{2}+16x+4-4x^{2}-6x-2$$

Combine 16x^{2} and -4x^{2} to get 12x^{2}.

$$12x^{2}+16x+4-6x-2$$

Combine 16x and -6x to get 10x.

$$12x^{2}+10x+4-2$$

Subtract 2 from 4 to get 2.

$$12x^{2}+10x+2$$

Expand

$$12x^{2}+10x+2$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4x+2\right)^{2}.

$$16x^{2}+16x+4-\left(x+1\right)\left(4x+2\right)$$

Use the distributive property to multiply x+1 by 4x+2 and combine like terms.

$$16x^{2}+16x+4-\left(4x^{2}+6x+2\right)$$

To find the opposite of 4x^{2}+6x+2, find the opposite of each term.

$$16x^{2}+16x+4-4x^{2}-6x-2$$

Combine 16x^{2} and -4x^{2} to get 12x^{2}.

$$12x^{2}+16x+4-6x-2$$

Combine 16x and -6x to get 10x.

$$12x^{2}+10x+4-2$$

Subtract 2 from 4 to get 2.

$$12x^{2}+10x+2$$