Question
Factorize the following expressions:$8x^3 - 125y^3 + 180xy + 216$
✓
Answer
$8x^3 - 125y^3 + 180xy + 216 or, 8x^3 - 125y^3+ 216 + 180xy$
$= (2x)^3 + (-5y)^3 + 6^3 - 3 \times (2x)(-5y)(6)$
$= (2x + (-5y) + 6)((2x)^2 + (-5y)^2 +6^2 - 2x(-5y) - (-5y)6 - 6(2x))$
$= (2x - 5y + 6)(4x^2 + 25y^2 + 36 + 10xy + 30y -12x)$
$\therefore$$ 8x^3 - 125y^3 + 180xy + 216$
$= (2x - 5y + 6)(4x^2 + 25y^2 + 36 + 10xy + 30y -12x)$
$= (2x)^3 + (-5y)^3 + 6^3 - 3 \times (2x)(-5y)(6)$
$= (2x + (-5y) + 6)((2x)^2 + (-5y)^2 +6^2 - 2x(-5y) - (-5y)6 - 6(2x))$
$= (2x - 5y + 6)(4x^2 + 25y^2 + 36 + 10xy + 30y -12x)$
$\therefore$$ 8x^3 - 125y^3 + 180xy + 216$
$= (2x - 5y + 6)(4x^2 + 25y^2 + 36 + 10xy + 30y -12x)$
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