Calculate the result of the following algebraic fraction when x = -2 and y = 2. — Armed Services Vocational Aptitude Battery (ASVAB)

Calculate the result of the following algebraic fraction when $x = -2$ and $y = 2$ .

Cevap:The evaluated value of the expression

\frac{4x^3 + 2y^2}{x - y}

is 【6】.

The correct answer is 6 because substituting the values

x = -2

and

y = 2

into the expression yields a numerator of

-24

and a denominator of

-4

. Dividing a negative by a negative results in a positive 6.

Substitute the given values for

x

and

y

into the expression.

\frac{4(-2)^3 + 2(2)^2}{-2 - 2}

Variable substitution is the first required step in evaluating any algebraic expression.

Evaluate the terms with exponents in the numerator.

(-2)^3 = -8

and

2^2 = 4

According to the order of operations (PEMDAS), exponents must be resolved before multiplication.

Perform the multiplication operations in the numerator.

4(-8) = -32

and

2(4) = 8

Multiplication is performed after exponents.

Add the resulting terms in the numerator and subtract the terms in the denominator.

Numerator:

-32 + 8 = -24

. Denominator:

-2 - 2 = -4

Simplify the numerator and denominator completely before dividing.

Divide the simplified numerator by the simplified denominator.

\frac{-24}{-4} = 6

Dividing a negative number by a negative number results in a positive quotient.

Evaluating algebraic expressions with negative integers and exponents

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