Factor $4x^{2} + 12x + 9$.
A$(2x + 3)(2x + 3) = (2x + 3)^{2}$
B$(4x + 3)(x + 3)$
C$(4x + 9)(x + 1)$
D$(2x - 3)^{2}$
Answer & Solution
Correct answer: A. $(2x + 3)(2x + 3) = (2x + 3)^{2}$
Identity $(a + b)^{2} = a^{2} + 2ab + b^{2}$ with $a = 2x$, $b = 3$:
$(2x)^{2} + 2(2x)(3) + 3^{2} = 4x^{2} + 12x + 9$ ✓.
So $4x^{2} + 12x + 9 = (2x + 3)^{2}$.
- Trap C has the wrong sign in the middle term.
- Trap B/D give different products that don't expand to the target.
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