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

$$( x + 2 ) ( x - 2 ) + ( x + 3 ) ( 3 - x )$$

Evaluate

$$5$$

Solution Steps

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}.

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

Calculate 2 to the power of 2 and get 4.

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

Consider \left(x+3\right)\left(3-x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$x^{2}-4+3^{2}-x^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}-4+9-x^{2}$$

Add -4 and 9 to get 5.

$$x^{2}+5-x^{2}$$

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

$$5$$

Factor

$$5$$