find 3ab+4bc+3ca-a²-b²-c²? if a=2, b=3, c=-2

asked by guest
on Nov 15, 2024 at 5:28 am



You asked:

Calculate the value of \(3 a b + 4 b c + 3 c a - {a}^{2} - {b}^{2} - {c}^{2}\) when \(a = 2\), \(b = 3\), and \(c = -2\).

MathBot Answer:

\[3 a b + 4 b c + 3 c a - {a}^{2} - {b}^{2} - {c}^{2} = -35\]

$$\begin{aligned}- a^{2} + 3 a b + 3 a c - b^{2} + 4 b c - c^{2}&=- \left(-2\right)^{2} - 2^{2} - 3^{2} + 3 \left(-2\right) 2 + 3 \cdot 3 \cdot 2 + 4 \left(-2\right) 3\\&=- \left(-2\right)^{2} - 3^{2} + 3 \left(-2\right) 2 + 3 \cdot 3 \cdot 2 + 4 \left(-2\right) 3 - 4\\&=- \left(-2\right)^{2} + 3 \left(-2\right) 2 + 3 \cdot 3 \cdot 2 + 4 \left(-2\right) 3 - 4 - 9\\&=- \left(-2\right)^{2} + 3 \left(-2\right) 2 + 3 \cdot 3 \cdot 2 + 4 \left(-2\right) 3 -9 - 4\\&=- \left(-2\right)^{2} + 3 \left(-2\right) 2 + 3 \cdot 3 \cdot 2 + 4 \left(-2\right) 3 -9 -4\\&=3 \left(-2\right) 2 + 3 \cdot 3 \cdot 2 + 4 \left(-2\right) 3 -9 -4 - 4\\&=3 \left(-2\right) 2 + 4 \left(-2\right) 3 -9 -4 + 18 - 4\\&=4 \left(-2\right) 3 -12 -9 -4 + 18 - 4\\&=-24 -12 -9 -4 + 18 - 4\\&=-35\end{aligned}$$


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