Question

If 3x+2y=16,xy=8 find 27x to power 3 + 8y to power 3

Answer 1

$27 {x}^{3} + 8 {y}^{3} = {(3x)}^{3} + {(2y)}^{3} \\ = { (3x + 2y)}^{3} - 3 \times 3x \times 2y \times (3x + 2y) \\ { (3x + 2y)}^{3} - 18xy \times (3x + 2y) \\ { 16}^{3} - 18 \times 8 \times 16 = 1792$