# Cebirsel ifadeler ve özdeşliklee

**URL:** <https://sorumatik.co/t/cebirsel-ifadeler-ve-ozdesliklee/159589>\
**Category:** LGS\
**Tags:** özdeşlikler, cebirsel-ifadeler, matematik\
**Created:** [Ocak 17, 2025, 12:12ös UTC](https://sorumatik.co/t/cebirsel-ifadeler-ve-ozdesliklee/159589 "2025-01-17T12:12:34Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Ibrahim\_Kiran](https://sorumatik.co/user_avatar/sorumatik.co/ibrahim_kiran/32/31936_2.png) [@Ibrahim\_Kiran](https://sorumatik.co/u/Ibrahim_Kiran)\
**Post date:** [Ocak 17, 2025, 12:12ös UTC](https://sorumatik.co/t/cebirsel-ifadeler-ve-ozdesliklee/159589/1 "2025-01-17T12:12:34Z")

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@sorumatikbot

 ![17371159178676730994726661331530](https://sorumatik.co/uploads/default/original/3X/0/7/073020c4af2b63d2b55320d90d6a7af10ac1e2ea.jpeg)

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**Author:** ![Sorumatik\_Ogretmen](https://sorumatik.co/user_avatar/sorumatik.co/sorumatik_ogretmen/32/30517_2.png) [@Sorumatik\_Ogretmen](https://sorumatik.co/u/Sorumatik_Ogretmen)\
**Post date:** [Ocak 17, 2025, 12:12ös UTC](https://sorumatik.co/t/cebirsel-ifadeler-ve-ozdesliklee/159589/2 "2025-01-17T12:12:56Z")

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**Algebraic Expressions and Identities: Problem-Solving with Rectangular Prism Geometry**

The problem at hand involves dissecting a rectangular prism-like wooden block into smaller pieces and finding the algebraic expression for the area of the top surface of one of those smaller pieces.

**Understanding the Dimensions**

The rectangular prism has the following dimensions:

- Length: ((8x + 20)) cm
- Width: ((x - 1)) cm

It’s mentioned that this wooden block is cut into **4 equal pieces** parallel to the shorter side. This means that the entire length ((8x + 20)) cm is divided into 4 parts.

**Calculating the Length of Each Small Piece**

Given that the division is parallel to the shorter side, the length of each smaller piece equals:

\text{Length of each small piece} = \frac{8x + 20}{4} \, \text{cm}

Now let’s simplify this expression:

1. Divide both terms in the numerator by 4:
  - ( \frac{8x}{4} = 2x )
  - ( \frac{20}{4} = 5 )

Thus, the length of each small piece is (2x + 5) cm.

**Finding the Area of the Top Surface of One Small Piece**

The area of the top surface of one small piece is found by multiplying its length by its width:

\text{Area of small piece} = (\text{length}) \times (\text{width}) = (2x + 5) \times (x - 1)

**Expanding the Expression**

To determine the expression for the area, expand this product using the distributive property (also known as FOIL method for binomials):

1. Multiply:

2. Combine all terms to get the final expression:

2x^2 - 2x + 5x - 5 = 2x^2 + 3x - 5

**Conclusion**

The algebraic expression for the area of the top surface of one of the smaller, equal pieces is (2x^2 + 3x - 5) square centimeters. The correct choice from the given options would be **D) 2x² + 3x - 5**.