If (8x3 + 27y3) ÷ (2x + 3y) = (Ax2 + Bxy + Cy2), then the value of (5A + 4B + 3C) is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 23
⇒ (8x3 + 27y3) ÷ (2x + 3y)
By using the identity, a3 + b3 = (a + b)(a2 + b2 + ab)
⇒ ((2x + 3y)(4x2 + 9y2 - 6xy))/(2x + 3y)
⇒ (4x2 + 9y2 - 6xy)
⇒ (Ax2 + Bxy + Cy2)
⇒ A = 4, B = -6 & C = 9
⇒ (5A + 4B + 3C) = 5(4) + 4(-6) + 3(9)
⇒ 20 - 24 + 27
⇒ 23