A mathematical model for a fluid dynamics problem reduces to the following algebraic expre… — Armed Services Vocational Aptitude Battery (ASVAB)

A mathematical model for a fluid dynamics problem reduces to the following algebraic expression:

-2xy(3x - 4y) - [5x^2y - 2xy(x + 3y)]

When completely simplified, which of the following represents the equivalent standard form?

A
$-13x^2y + 2xy^2$
B
$-9x^2y + 2xy^2$
$-9x^2y + 14xy^2$ Answer
D
$5x^3y^3$

Answer

The correct expression is

-9x^2y + 14xy^2

The correct expression is derived by applying the order of operations and the distributive property. First, evaluate the terms inside the brackets to get

3x^2y - 6xy^2

. Then expand the initial term to

-6x^2y + 8xy^2

. Subtracting the bracket flips the inner signs, yielding

-6x^2y + 8xy^2 - 3x^2y + 6xy^2

. Combining like terms results in

-9x^2y + 14xy^2

Step-by-Step Solution

Expand the inner terms inside the brackets by distributing

-2xy

(x + 3y)

5x^2y - 2x^2y - 6xy^2

Following the order of operations, simplify grouping symbols first.

Combine like terms within the brackets.

3x^2y - 6xy^2

To minimize the expression before subtracting it from the leading terms.

Distribute

-2xy

to the terms in the first parenthesis

(3x - 4y)

-6x^2y + 8xy^2

To expand the first part of the expression.

Subtract the simplified bracketed expression from the expanded first part.

-6x^2y + 8xy^2 - (3x^2y - 6xy^2) = -6x^2y + 8xy^2 - 3x^2y + 6xy^2

To remove the remaining grouping symbols and properly distribute the negative sign.

Combine the remaining like terms to reach the final form.

-9x^2y + 14xy^2

To express the polynomial in its simplest standard form.

Key Concept

Simplifying complex expressions using the distributive property, managing negative multipliers, and working with nested grouping symbols.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic