Factor completely: 36x^2y - 48xy + 16y.
A4y(3x-2)(3x-2)
B4y(3x+2)(3x+2)
C4y(3x-4)(3x-1)
D4y(9x-2)(x-2)
Answer & Solution
Correct answer: A. 4y(3x-2)(3x-2)
1. Factor out the GCF first: 36x squared y - 48xy + 16y has a common factor of 4y, giving 4y(9x squared - 12x + 4).
2. Check whether 9x squared - 12x + 4 is a perfect square trinomial: 9x squared is (3x) squared, 4 is 2 squared, and twice the product of 3x and 2 is 12x, which matches.
3. Write the square of the binomial inside the parentheses: 4y(3x - 2)(3x - 2).
4. Check by multiplying: 4y times (9x squared - 6x - 6x + 4) gives back 36x squared y - 48xy + 16y.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.4 Factor Special Products_
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