Solve (x+4)^2-(x-2)(x+2)

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

Evaluate

$$8x+20$$

Solution Steps

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

$$x^{2}+8x+16-\left(x-2\right)\left(x+2\right)$$

Consider \left(x-2\right)\left(x+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

$$x^{2}+8x+16-\left(x^{2}-4\right)$$

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

$$x^{2}+8x+16-x^{2}+4$$

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

$$8x+16+4$$

Add 16 and 4 to get 20.

$$8x+20$$

Expand

$$8x+20$$

Solution Steps

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

$$x^{2}+8x+16-\left(x-2\right)\left(x+2\right)$$

Consider \left(x-2\right)\left(x+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

$$x^{2}+8x+16-\left(x^{2}-4\right)$$

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

$$x^{2}+8x+16-x^{2}+4$$

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

$$8x+16+4$$

Add 16 and 4 to get 20.

$$8x+20$$