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
$-9x^2y + 2xy^2$
$-9x^2y + 14xy^2$ Cevap
D
$5x^3y^3$

Cevap

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

Adım Adım Çözüm

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.

Anahtar Kavram

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

Soru

Cevap

Adım Adım Çözüm

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