Simplify \(\frac{8x^3 + 27y^3 - 64z^3 + 72xyz}{4x^2 + 9y^2 + 16z^2 - 6xy + 12yz + 8zx}\)

Question

Question

This question was previously asked in

RRB NTPC Graduate Level CBT-I Official Paper (Held On: 06 Jun, 2025 Shift 3)

Answer 1

Given:

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).

Download Solution PDF