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Question: Factor the trinomial.
5x2 - 32xy - 64y2
A ) (x - 8y)(x - 8y)
B ) (5x + 8y)(x - 8y)
C ) (x + y)(5x + 64y)
D ) (x + 8y)(5x - 8y)
Steps to derive
1 5x2 - 32xy - 64y2
[Given trinomial.]
2 a = 5, b = - 32, c = - 64
3 Find two numbers whose product is 5 and another two numbers whose product is - 64.
Factors of 5 Factors of - 64
1, 5 1, - 64 and 8, - 8
4 Use FOIL method to check the middle term in the trial factors.
Trial factors Middle term
(x + y)(5x - 64y) - 64xy + 5xy = - 59xy
(x + 8y)(5x - 8y) - 8xy + 40xy = 32xy
(5x + 8y)(x - 8y) - 40xy + 8xy = - 32xy
5 So, 5x2 - 32xy - 64y2 = (5x + 8y)(x - 8y).
Hence the right answer is Option B
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