If x = -3 and y = 2, what is the value of the algebraic expression \frac{x^2 y - (x - y)^2… — ACT

If $x = -3$ and $y = 2$ , what is the value of the algebraic expression $\frac{x^2 y - (x - y)^2}{2x + y^2}$ ?

\frac{7}{2}

Substituting

x = -3

and

y = 2

gives a numerator of

(-3)^2(2) - (-3 - 2)^2 = 18 - 25 = -7

and a denominator of

2(-3) + 2^2 = -6 + 4 = -2

. Dividing

-7

-2

gives

\frac{7}{2}

Evaluate the terms in the numerator

x^2 y = (-3)^2(2) = 9 \cdot 2 = 18

and

(x - y)^2 = (-3 - 2)^2 = (-5)^2 = 25

Apply order of operations by performing parenthetical subtraction before squaring negative numbers.

Subtract the terms to find the total numerator value

18 - 25 = -7

Subtract the squared binomial result from the first product.

Evaluate the denominator

2x + y^2 = 2(-3) + 2^2 = -6 + 4 = -2

Multiply and square the variable values before adding.

Divide the numerator by the denominator and simplify

\frac{-7}{-2} = \frac{7}{2}

Dividing a negative number by a negative number yields a positive result.

Evaluating Algebraic Expressions with Negative Bases and Parentheses

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