Question
Download Solution PDFSimplify \(\frac{8x^3 + 27y^3 - 64z^3 + 72xyz}{4x^2 + 9y^2 + 16z^2 - 6xy + 12yz + 8zx}\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Simplify \(\frac{8x^3 + 27y^3 - 64z^3 + 72xyz}{4x^2 + 9y^2 + 16z^2 - 6xy + 12yz + 8zx}\)
Formula used:
(a3 + b3 + c3 - 3abc)/(a2 + b2 + c2 - ab - bc - ca) = (a + b + c)
Where, a = 2x, b = 3y, c = -4z
Calculation:
Numerator = 8x3 + 27y3 - 64z3 + 72xyz
⇒ Numerator = (2x)3 + (3y)3 + (-4z)3 - 3(2x)(3y)(-4z)
⇒ Numerator = a3 + b3 + c3 - 3abc
Denominator = 4x2 + 9y2 + 16z2 - 6xy + 12yz + 8zx
⇒ Denominator = (2x)2 + (3y)2 + (-4z)2 - (2x)(3y) - (3y)(-4z) - (-4z)(2x)
⇒ Denominator = a2 + b2 + c2 - ab - bc - ca
⇒ Expression = (a + b + c)
⇒ Expression = (2x + 3y - 4z)
∴ The correct answer is option (1).
Last updated on Jul 17, 2025
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