Factorize the following expressions: 125 + 8x3 - 27y3 + 90xy - Vidyadip

Question

Factorize the following expressions:
125 + 8x³ - 27y³ + 90xy

✓

Answer

125 + 8x³ - 27y³ + 90xy
= 5³ + (2x)³ + (-3y)³ - 3 × 5 × 2x × (-3y)
= (5 + 2x + (-3y))(5² + (2x)² + (-3y)² - 5(2x) - 2x(-3y) - (-3y)5)
= (5 + 2x + -3y)(25 + 4x² + 9y² - 10x + 6xy + 15y)
$\therefore$ 125 + 8x³ - 27y³ + 90xy
= (5 + 2x + -3y)(25 + 4x² + 9y² - 10x + 6xy + 15y)

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