Question

what value of ( a ) will make the following equation true? ( (x + a)(x - a) = x^2 - 16 ) ( a = 8 ) ( a = 16 ) ( a = 4 ) ( a = 2 )

Explanation:

Step1: Apply difference of squares rule

Recall that $(x+a)(x-a)=x^2-a^2$

Step2: Set equal to given right-hand side

$x^2-a^2 = x^2-16$

Step3: Solve for $a^2$

Subtract $x^2$ from both sides: $-a^2=-16$, so $a^2=16$

Step4: Find positive $a$ value

Take square root: $a=\sqrt{16}=4$

Answer:

a = 4