Evaluate the algebraic expression 3x^2 - 2xy + y^2 for x = -3 and y = -2. — ACT

Evaluate the algebraic expression $3x^2 - 2xy + y^2$ for $x = -3$ and $y = -2$ .

Answer:The value of the expression

3x^2 - 2xy + y^2

when

x = -3

and

y = -2

is 【19】.

Substituting

x = -3

and

y = -2

into

3x^2 - 2xy + y^2

yields

3(-3)^2 - 2(-3)(-2) + (-2)^2 = 3(9) - 12 + 4 = 27 - 12 + 4 = 19

Substitute

x = -3

and

y = -2

into the expression

3(-3)^2 - 2(-3)(-2) + (-2)^2

Replace each variable with its assigned value, using parentheses to properly preserve negative signs.

Evaluate the exponent terms

3(9) - 2(-3)(-2) + 4

Follow the order of operations (PEMDAS) by evaluating powers first:

(-3)^2 = 9

and

(-2)^2 = 4

Perform the multiplications

27 - 12 + 4

Multiply the numerical factors:

3 \times 9 = 27

and

-2 \times (-3) \times (-2) = -12

Perform addition and subtraction from left to right

19

Subtract

12

from

27

to get

15

, then add

4

to arrive at

19

Evaluating Algebraic Expressions with Negative Values

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