An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

Identify like terms in the polynomial expression.
Group the like terms together: ( 10 x 2 y − 4 x 2 y ) + 2 x y 2 − 4 x 2 = 6 x 2 y + 2 x y 2 − 4 x 2 .
Check each option to see if it matches the grouped expression, focusing on explicit grouping of like terms.
The correct expression is ( − 4 x 2 ) + 2 x y 2 + [ 10 x 2 y + ( − 4 x 2 y ) ] , which groups the like terms 10 x 2 y and − 4 x 2 y together. ( − 4 x 2 ) + 2 x y 2 + [ 10 x 2 y + ( − 4 x 2 y ) ] ​

Explanation

Understanding the Problem We are given the polynomial expression 10 x 2 y + 2 x y 2 − 4 x 2 − 4 x 2 y and asked to identify the expression that correctly groups like terms together.

Identifying Like Terms First, let's identify the like terms in the given polynomial expression. The like terms are terms with the same variables raised to the same powers. In this expression, the like terms are 10 x 2 y and − 4 x 2 y . The other terms are 2 x y 2 and − 4 x 2 .

Grouping Like Terms Now, let's group the like terms together. We have ( 10 x 2 y − 4 x 2 y ) + 2 x y 2 − 4 x 2 . Simplifying the like terms, we get 6 x 2 y + 2 x y 2 − 4 x 2 .

Checking Each Option Now, let's examine each option to see if it matches our grouped expression:


Option 1: ​ ( − 4 x 2 ) + ( − 4 x 2 y ) + 10 x 2 y ​ + 2 x y 2 = ∣ − 4 x 2 + 6 x 2 y ∣ + 2 x y 2 . This does not match because of the absolute value.
Option 2: 10 x 2 y + 2 y 2 + ​ ( − 4 x 2 ) + ( − 4 x 3 y ) ​ = 10 x 2 y + 2 y 2 + ∣ − 4 x 2 − 4 x 3 y ∣ . This does not match because of the 2 y 2 term and the absolute value.
Option 3: ( − 4 x 2 ) + 2 x y 2 + [ 10 x 2 y + ( − 4 x 2 y ) ] = − 4 x 2 + 2 x y 2 + [ 6 x 2 y ] = − 4 x 2 + 2 x y 2 + 6 x 2 y . This matches our simplified expression.
Option 4: { 10 x 2 y + 2 x y 2 + ( − 4 x 2 y ) } + ( − 4 x 2 ) = 6 x 2 y + 2 x y 2 + ( − 4 x 2 ) = 6 x 2 y + 2 x y 2 − 4 x 2 . This also matches our simplified expression.

Selecting the Best Option Both Option 3 and Option 4 match our simplified expression. However, the question asks for the expression that shows the sum of the polynomials with like terms grouped together . Option 3, ( − 4 x 2 ) + 2 x y 2 + [ 10 x 2 y + ( − 4 x 2 y ) ] , explicitly groups the like terms 10 x 2 y and − 4 x 2 y within the brackets. Option 4, { 10 x 2 y + 2 x y 2 + ( − 4 x 2 y ) } + ( − 4 x 2 ) , groups 10 x 2 y , 2 x y 2 , and − 4 x 2 y together, but it doesn't isolate just the like terms. Therefore, Option 3 is the better answer.

Final Answer The expression that shows the sum of the polynomials with like terms grouped together is ( − 4 x 2 ) + 2 x y 2 + [ 10 x 2 y + ( − 4 x 2 y ) ] .


Examples
Grouping like terms is a fundamental concept in algebra that simplifies expressions and makes them easier to work with. In real life, this can be applied to various situations, such as inventory management. Imagine a store that sells different types of products. By grouping similar items (like terms), the store can easily calculate the total quantity of each product, manage stock levels, and make informed decisions about ordering and pricing. For example, if the store has 10x^2y of one product and -4x^2y of the same product returned, they can quickly determine the net quantity available.

Answered by GinnyAnswer | 2025-07-08

Approximately 2.81 × 1 0 21 electrons flow through the electric device delivering a current of 15.0 A over 30 seco n d s .
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Answered by Anonymous | 2025-08-14