alleryStart learning →Factor: x^2 + 12xy + 36y^2.
A(x+4y)(x+9y)
B(x+3y)(x+12y)
C(x+6y)(x+6y)
D(x-6y)(x-6y)
Answer & Solution
Correct answer: C. (x+6y)(x+6y)
1. Since the last term has y squared, the second term of each binomial factor must contain y.
2. Find two numbers that multiply to 36 and add to 12.
3. Testing the factor pairs of 36, the pair 6 and 6 multiplies to 36 and adds to 12.
4. Use 6 and 6 as the coefficients of y to get (x + 6y)(x + 6y), and check: x squared + 6xy + 6xy + 36y squared gives back x squared + 12xy + 36y squared.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.2 Factor Quadratic Trinomials with Leading Coefficient 1_
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