Question

Factorize 8x3+27y3+36x2y+ 54xy2

Answer 1

$8 {x}^{3} + 27 {y}^{3} + 36 {x}^{2} y + 54x {y}^{2}$

$= {(2x)}^{3} + {(3y)}^{3} + 3 \times {(2x)}^{2} \times 3y + 3 \times 2x \times {(3y)}^{2}$

$= {(2x + 3y)}^{3}$

Identity used here:-

${(x + y)}^{3} = {x}^{3} + {y}^{3} + 3 {x}^{2} y + 3x {y}^{2}$