Question

Find the value of 27x^3 - 64y^3 - 108x^2y + 144xy^2 if x = 3 and y 2.
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Answer 1

Step-by-step explanation:

27x3−64y3=108x2y−144xy2

We seek r=x/y, so x=ry

27r3y3−64y3=108r2y3−144ry3

Assuming y≠0,

27r3−64=108r2−144r

27r3−108r2+144r−64=0

27 is a cube as is −64 and 108 and 144 have only prime factors of 2 and 3. Let’s guess this is:

0=(3r−4)3=33r3−3(3r)2(4)+3(3r)(4)2−43=27r3−108r2+144r−64✓

Good guess. r=4/3

Answer: x:y=4:3

Answer 2

Answer:

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