Math  /  Algebra

QuestionSort the expressions into the categories with which they are equal. Note that some expressions may not belong to any of the categories. 2(y+3)2(y+3) 4(y3)4(y-3) 4y8+2y44 y-8+2 y-4
Equal to 5y5 y - 10 Equal to 3(2y4)3(2 y-4) Equal to 2y2 y - 6 5(y2)5(y-2) 6(y2)6(y-2) 2(y3)2(y-3)

Studdy Solution

STEP 1

What is this asking? We need to simplify each expression and see which ones are equal to each other! Watch out! Don't forget to distribute correctly and combine like terms carefully.
It's easy to make a small mistake that messes everything up!

STEP 2

1. Simplify and categorize the expressions.

STEP 3

Distribute the **2** to both terms inside the parentheses.
Remember, distributing means multiplying each term inside the parentheses by the term outside.
This gives us 2y+232 \cdot y + 2 \cdot 3, which simplifies to 2y+62y + 6.
This doesn't match any of our categories.

STEP 4

Distribute the **4** to get 4y434 \cdot y - 4 \cdot 3, which simplifies to 4y124y - 12.
This doesn't match any of the categories either.

STEP 5

Combine the **yy terms** to get 4y+2y=6y4y + 2y = 6y.
Combine the **constant terms** to get 84=12-8 - 4 = -12.
So the simplified expression is 6y126y - 12.
Hey, this is equal to 6(y2)6(y-2)!
We found a match!

STEP 6

Distribute the **5** to get 5y525 \cdot y - 5 \cdot 2, which simplifies to 5y105y - 10.
This matches the category "Equal to 5y105y - 10"!

STEP 7

Distribute the **6** to get 6y626 \cdot y - 6 \cdot 2, which simplifies to 6y126y - 12.
This matches the category "Equal to 6(y2)6(y-2)"!

STEP 8

Distribute the **2** to get 2y232 \cdot y - 2 \cdot 3, which simplifies to 2y62y - 6.
This matches the category "Equal to 2y62y - 6"!

STEP 9

Let's distribute the **3** to get 32y343 \cdot 2y - 3 \cdot 4, which simplifies to 6y126y - 12.
This also matches the category "Equal to 6(y2)6(y-2)"!

STEP 10

* **Equal to 5y105y - 10:** 5(y2)5(y-2) * **Equal to 6(y2)6(y-2):** 4y8+2y44y - 8 + 2y - 4, 6(y2)6(y-2), 3(2y4)3(2y - 4) * **Equal to 2y62y - 6:** 2(y3)2(y-3) * **Don't belong to any category:** 2(y+3)2(y+3), 4(y3)4(y-3)

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