Question

which expression is equivalent to ((x + 3)(x + 3))?
a (x + 3^2)
b (2(x + 3))
c (x^2 + 3^2)
d (2x + 9)
e ((x + 3)^2)

Explanation:

Step1: Recall the definition of squaring a binomial

The expression \((a + b)(a + b)\) is equivalent to \((a + b)^2\) by the definition of exponentiation (where squaring a number or expression means multiplying it by itself). Here, \(a = x\) and \(b = 3\), so \((x + 3)(x + 3)\) should be equivalent to \((x + 3)^2\).

Step2: Analyze other options (optional but for clarity)

• Option A: \(x+3^2=x + 9\), which is not equal to \((x + 3)(x + 3)=x^2+6x + 9\).
• Option B: \(2(x + 3)=2x+6\), not equal to \((x + 3)(x + 3)\).
• Option C: \(x^2+3^2=x^2 + 9\), which is missing the middle term \(6x\) compared to \((x + 3)(x + 3)=x^2+6x + 9\).
• Option D: \(2x + 9\) is not equal to \((x + 3)(x + 3)\).
• Option E: \((x + 3)^2\) is equal to \((x + 3)(x + 3)\) as shown in Step 1.

Answer:

E. \((x + 3)^2\)