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Chapter 6: Problem 30

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

Short Answer

Expert verified
The value of the expression \(4x^2 + 3xy + 2y^2\) for \(x=3\) and \(y=2\) is 62.

Step by step solution

01

Substitute the given values into the algebraic expression

Replace \(x\) with 3 and \(y\) with 2 in the expression \(4x^2 + 3xy + 2y^2\). This gives \(4(3)^2 + 3(3)(2) + 2(2)^2\).
02

Carry out the operations

Calculate each term in the expression: \(4(3)^2 = 4 * 9 = 36\), \(3(3)(2) = 3 * 3 * 2 = 18\), and \(2(2)^2 = 2 * 4 = 8\). The expression becomes \(36 + 18 + 8\).
03

Add all terms

Sum the values of the calculated expressions: \(36 + 18 + 8 = 62\).

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I began the solution of \(5-3(x+2)>10 x\) by simplifying the left side, obtaining \(2 x+4>10 x\).

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Solve each equation by the method of your choice. \(7 x(x-2)=3-2(x+4)\)

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