Question

1. which of the following expressions simplify to $x^2 - 9$?

i. $(x - 3)(x + 3)$
ii. $(x - 3)^2$
iii. $(x + 3)^2$
a. i only
b. ii only
c. i and ii
d. i, ii or iii

Explanation:

Step1: Simplify Expression I

Using the difference of squares formula \((a - b)(a + b)=a^2 - b^2\), for \((x - 3)(x + 3)\), let \(a = x\) and \(b = 3\). Then \((x - 3)(x + 3)=x^2-3^2=x^2 - 9\).

Step2: Simplify Expression II

Using the perfect square formula \((a - b)^2=a^2-2ab + b^2\), for \((x - 3)^2\), let \(a = x\) and \(b = 3\). Then \((x - 3)^2=x^2-2\times x\times3 + 3^2=x^2-6x + 9\), which is not equal to \(x^2 - 9\).

Step3: Simplify Expression III

Using the perfect square formula \((a + b)^2=a^2+2ab + b^2\), for \((x + 3)^2\), let \(a = x\) and \(b = 3\). Then \((x + 3)^2=x^2+2\times x\times3 + 3^2=x^2+6x + 9\), which is not equal to \(x^2 - 9\).

Answer:

a. I only