91Ó°ÊÓ

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. For example, in the expression \( -5t + 13s + 8t - 3s \), each term like \( -5t \) or \( 13s \) is called a 'monomial.' When we combine these terms, we form a polynomial. Polynomials can have many terms, but each term is a product of a constant and a variable raised to a non-negative integer power.
Understanding polynomials is essential because they are used in many areas of mathematics and science. They help us to model and solve real-world problems. In our example, we combine terms with the same variable to simplify the polynomial. This makes it easier to work with and understand.

Adding and subtracting algebraic expressions involves combining like terms. Like terms have the same variable raised to the same power. In the expression \( (-5t + 13s) + (8t - 3s) \), identifying and properly aligning the like terms is crucial.
Here's a simple process to follow:

• Identify like terms: Look for terms with the same variables and powers.
• Align like terms: Arrange them so that they are easy to combine.
• Combine like terms: Add or subtract the coefficients (numbers in front of the variables).

For example, in our problem:

• Identify: Like terms are \( -5t \) and \( 8t \); \( 13s \) and \( -3s \).
• Align: Rearrange to make it visually clear, if needed.
• Combine: \( -5t + 8t = 3t \) and \( 13s - 3s = 10s \).

This process simplifies the expression to \( 3t + 10s \).

Simplifying algebraic expressions is about making them as easy to work with as possible. This often means combining like terms and reducing the expression to its simplest form. In our given problem, the expression \( -5t + 13s + 8t - 3s \) can be simplified significantly.
Simplification involves:

• Combining like terms efficiently to reduce the number of terms.
• Ensuring the expression is left in its simplest form, with all like terms combined.

For the expression \( -5t + 13s + 8t - 3s \):

• Combine like terms: \( -5t \) and \( 8t \) give \( 3t \); \( 13s - 3s \) gives \( 10s \).

Thus, the simplified expression is \( 3t + 10s \). This form is much easier to use in further calculations or problem-solving.