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Chapter 6: Problem 31

Evaluate the algebraic expression for the given value or values of the variables. \(-x^{2}-4 x y+3 y^{3} ; \quad x=-1, y=-2\)

Short Answer

Expert verified
The value of the algebraic expression \(-x^{2}-4 x y+3 y^{3}\) for \(x=-1\) and \(y=-2\) is \(-33\).

Step by step solution

01

Substitute Values

Substitute \(x=-1\) and \(y=-2\) into the original equation \(-x^{2}-4 x y+3 y^{3}\). This gives \(-(-1)^{2}-4(-1)(-2)+3(-2)^{3}\).
02

Apply order of operations (Exponents)

Evaluate the exponents first according to the order of operations. You have \(-1^{2}=1\) and \(-2^{3}=-8\). So the equation simplifies to \[-1-4(-1)(-2)+3(-8)\].
03

Apply order of operations (Multiplication and Division)

Next, do the multiplication. You have \(-4(-1)(-2) = -8\) and \(3(-8) = -24\). The equation simplifies further to \[-1 - 8 - 24\].
04

Apply order of operations (Addition and Subtraction)

Now perform the remaining additions and subtractions. \[-1 - 8 - 24 = -33\].

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Most popular questions from this chapter

Solve the quadratic equations by factoring. \(3 x^{2}-4 x=15\)

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