Question

2x+3y=15 and xy=6 find 8xraise to power 3 and 27yraise to power 3

Answer 1

$8 {x}^{3} + 27 {y}^{3} = ( {2x)}^{3} + ( {3y)}^{3} \\ = (2x + 3y)(4 {x}^{2} - 6xy + 9 {y}^{2} ) \\ = 15(4 {x}^{2} + 9 {y}^{2} + 12xy - 6xy - 12xy) \\ = 15(( {2x + 3y)}^{2} - 18xy) \\ = 15(( {15)}^{2} - 18 \times 6) \\ \\ = 15(225 - 108) \\ = 15 \times 117 \\ = 1755$