Discussion
What is the value of \(a(a + b^{2} + c) + b^{2}(a^{2} + b^{2} + c^{2}) - c(a + b^{2})\), when a = 1, b = −3 and c = −2 ?
Answer: B
The value is 154.
With a = 1, b = −3, c = −2, note that \(b^{2} = 9\) (the square of a negative number is positive):
\[ \begin{aligned} a(a + b^{2} + c) &= 1(1 + 9 - 2) = 8 \\ b^{2}(a^{2} + b^{2} + c^{2}) &= 9(1 + 9 + 4) = 126 \\ -c(a + b^{2}) &= 2(1 + 9) = 20 \end{aligned} \]
The total is 8 + 126 + 20 = 154. Treating the last term as \(-20\) (forgetting that \(-c = +2\)) gives 114, and 138 and 176 come from other sign slips.
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