Question

Is 5 x minus 4 Y is equal to 7 and X Y is equal to 8 find 125 x cube minus 64 y cube

Answer 1

Answer:

2583

Step-by-step explanation:

5x-4y=7

xy=8

125x³-64y³

Because of the difference of cubes, we know that x³-y³=(x-y)(x²+xy+y²)

Therefore, 125x³-64y³=(5x-4y)(25x²+20xy+16y²)

We also know that 25x²-20xy+16y²=(5x-4y)², which is 49.

To find 25x²+20xy+16y², we add 40xy on both sides of the equation 25x²-20xy+16y²=49, which would be 25x²+20xy+16y²=49+40xy, or 369 since we know xy=8 and 8·40 is equal to 320.

Now we can solve through substitution.

125x³-64y³=(5x-4y)(25x²+20xy+16y²)

125x³-64y³=7·369

125x³-64y³=2583