Multiple choice

Which of the following expressions represents the value of $\frac{8x^3 + 3x^2y + 2y}{x+y}$ at x = – 1 and y = 2?

  1. 7

  2. 2

  3. 5

  4. None of these
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B Correct answer
Explanation

$\frac{8(x)^3 + 3(x)^2y + 2y}{x+y}$ = $\frac{8(-1)^3 + 3(-1)^2y + 2y}{-1+y}$ = $\frac{8(-1)^3 + 3(-1)^2 2 + 2(2)}{-1+2}$ = $\frac{8(-1) + 6 + 4}{1}$ = – 8 + 6 + 4 = 2

AI explanation

Substituting x = -1 and y = 2 into 8x^3 + 3x^2y + 2y gives 8(-1) + 3(1)(2) + 2(2) = -8 + 6 + 4 = 2. Each term is evaluated separately before summing, and x^2 = 1 removes the sign issue from squaring a negative number, while x^3 keeps the negative sign.

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