Which expression shows the sum of the polynomials with like terms grouped together?

$10 x^2 y+2 x y^2-4 x^2-4 x^2 y$

A$\left(-4 x^2\right)+2 x y^2+\left[10 x^2 y+\left(-4 x^2 y\right)\right]$
B$10 x^2 y+2 x y^2+\left[\left(-4 x^2\right)+\left(-4 x^2 y\right)\right]$
C$\left[10 x^2 y+2 x y^2+\left(-4 x^2 y\right)\right]+\left(-4 x^2\right)$
D$\left[\left(-4 x^2\right)+\left(-4 x^2 y\right)+10 x^2 y\right]+2 x y^2$

Question

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04-11-2026
Mathematics

Answered

Which expression shows the sum of the polynomials with like terms grouped together?

$10 x^2 y+2 x y^2-4 x^2-4 x^2 y$

A$\left(-4 x^2\right)+2 x y^2+\left[10 x^2 y+\left(-4 x^2 y\right)\right]$
B$10 x^2 y+2 x y^2+\left[\left(-4 x^2\right)+\left(-4 x^2 y\right)\right]$
C$\left[10 x^2 y+2 x y^2+\left(-4 x^2 y\right)\right]+\left(-4 x^2\right)$
D$\left[\left(-4 x^2\right)+\left(-4 x^2 y\right)+10 x^2 y\right]+2 x y^2$

Verified Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-04T11:52:39-05:00

Identify the terms of the polynomial: $10x^2y$, $2xy^2$, $-4x^2$, and $-4x^2y$.
Recognize that $10x^2y$ and $-4x^2y$ are the only like terms because they share the same variable part $x^2y$.
Evaluate the options to find the one where $10x^2y$ and $-4x^2y$ are grouped together.
Conclude that the correct expression is $\boxed{a}$.

Explanation

Identifying Like Terms

The given expression is $10 x^2 y + 2 x y^2 - 4 x^2 - 4 x^2 y$. To group like terms together, we first identify them. Like terms are terms that share the same variables raised to the same exponents. Looking at the expression, we can identify the following terms:

$10 x^2 y$
$2 x y^2$
$-4 x^2$
$-4 x^2 y$

Comparing these terms, we see that $10 x^2 y$ and $-4 x^2 y$ both have the variables $x^2 y$. Therefore, these are the like terms that should be grouped together. The other terms, $2 x y^2$ and $-4 x^2$, do not have any like terms within the given expression.

Evaluating the Options

Now we look at the provided options to see which one correctly gathers the like terms ($10x^2y$ and $-4x^2y$) while keeping the other terms separate.

Option a: $(-4 x^2) + 2 x y^2 + [10 x^2 y + (-4 x^2 y)]$
Option b: $10 x^2 y + 2 x y^2 + [(-4 x^2) + (-4 x^2 y)]$
Option c: $[10 x^2 y + 2 x y^2 + (-4 x^2 y)] + (-4 x^2)$
Option d: $[(-4 x^2) + (-4 x^2 y) + 10 x^2 y] + 2 x y^2$

In option a, the terms $10 x^2 y$ and $-4 x^2 y$ are placed together inside the brackets. The other terms, $-4 x^2$ and $2 x y^2$, are outside, which correctly represents the original expression with the like terms grouped. The other options either include unlike terms inside the brackets or leave out one of the like terms from the group. Thus, option a is the correct choice.

Examples

Grouping like terms is a fundamental skill in algebra used whenever you need to simplify complex equations. For example, if you are modeling the total cost of materials for a project where you have different types of wood ($x^2y$) and metal fittings ($xy^2$), you can group the costs for the same materials to make your calculations easier and more efficient. By simplifying expressions in this way, you can clearly see the total quantities of each resource, allowing for better planning and management.