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Problem 134

Evaluate the expression $3 \mathrm{x}^{2} \mathrm{y}-2 \mathrm{xy}^{2} z+\mathrm{xyz}$$when$$\mathrm{X}=2$ $$\mathrm{Y}=-1$$, and $$\mathrm{z}=3$$

Expert verified
After substituting the values x = 2, y = -1, and z = 3 into the expression $$3x^2y - 2xy^2z + xyz$$, and simplifying, we get the final answer of $$-30$$.
See the step by step solution

Step 1: Write the given expression

The expression given is: $$3x^2y - 2xy^2z + xyz$$

Step 2: Substitute the values of x, y, and z

We are given the following values for x, y, and z: - x = 2 - y = -1 - z = 3 Substitute these values into the expression: $$3(2)^2(-1) - 2(2)(-1)^2(3) + (2)(-1)(3)$$

Step 3: Simplify the expression

Evaluate the expression step by step: 1. Evaluate exponents: $$3(4)(-1) - 2(2)(1)(3) + (2)(-1)(3)$$ 2. Perform multiplication: $$-12 - 12 - 6$$ 3. Perform addition and subtraction: $$-12 - 12 - 6 = -30$$

Step 4: Write the final answer

After evaluating the expression with the given values of x, y, and z, our final answer is -30.

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