Question

find the value of 27xcube +8ycube, if 3x+2y=14 and xy= 8

Answer 1

$27x ^{3 } + 8y ^{3} \\ = (3x) ^{3} + (2y) ^{3} \\ = 3x ^{3 } + 2y ^{3} + 3(3x)(2y)(3x + 2y) \\ =( 3x + 2y) {}^{3} + 54xy + \\ 36xy$

then put the value of 3x+2y and xy

$(14) {}^{3} + 90 \times 8 \ \\ = 2744 + 720 \\ = 3464$