Factor completely: 8x^2y - 98y.
A2y(2x-7)(2x-7)
B2y(4x-49)(x+1)
C8y(x-7)(x+7)
D2y(2x-7)(2x+7)
Answer & Solution
Correct answer: D. 2y(2x-7)(2x+7)
1. Factor out the GCF first: 8x squared y - 98y has a common factor of 2y, giving 2y(4x squared - 49).
2. Check whether 4x squared - 49 is a difference of squares: 4x squared is (2x) squared, and 49 is 7 squared, so it fits.
3. Factor the difference of squares as the product of conjugates: (2x - 7)(2x + 7).
4. The complete factorization is 2y(2x - 7)(2x + 7), and checking by multiplying confirms it expands back to 8x squared y - 98y.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.4 Factor Special Products_
Related questions
Factor: x^3 + 64.According to the Sum and Difference of Cubes Pattern, how does a^3+b^3 factor?Factor completely: 36x^2y - 48xy + 16y.Factor completely: 6x^2 + 96.What happens when you try to factor a sum of squares like a^2 + b^2?What is the completely factored form of x^4 - y^4?Factor: 100 - h^2.Factor: 121x^2 - 49y^2.