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Understanding like terms is a fundamental concept in polynomial addition. Like terms are terms that contain the same variables raised to the same power.
For example, in the expression \((7x^2 + 2x - 9) + (-3x^2 + 5)\), the terms \(7x^2\) and \(-3x^2\) are like terms because both terms involve \(x^2\).
Similarly, the constants \(-9\) and \(5\) are considered like terms because they do not involve any variables.

• The variables must be identical, including their exponents, to be considered like terms. This means \(x^2\) and \(x\) are not like terms because their exponents differ.
• Recognizing like terms is crucial because it allows you to appropriately combine them by performing operations on their coefficients.

Combining terms is the process of adding or subtracting the coefficients of like terms. Once you've recognized which terms in your polynomial are like terms, you can simplify your expression by adding the coefficients together.
This process streamlines the expression into a simpler form without changing its value. Let's revisit the expression \((7x^2 + 2x - 9) + (-3x^2 + 5)\):

• Combine the \(x^2\) terms: \(7x^2 + (-3x^2)\) which simplifies to \((7-3)x^2 = 4x^2\).
• The term \(2x\) doesn't have a corresponding like term in the second polynomial, so it remains unchanged in the expression.
• Add the constant terms: \(-9 + 5\) which simplifies to \(-4\).

After combining all like terms, the expression becomes \(4x^2 + 2x - 4\).

The concept of coefficients combination involves adjusting the numerical part of the terms in a polynomial. The coefficients are the numbers in front of the variables, which indicate how many of each term you have.

How to Combine Coefficients:

When you combine like terms, you actually just deal with these coefficients:

• Add or subtract the coefficients of like terms according to their signs. Positive and negative signs affect the operation performed.

In the previous polynomial example, consider:

• \(7x^2\) and \(-3x^2\): you add them by adding the coefficients 7 and -3, resulting in 4 (i.e., \((7 - 3)x^2 = 4x^2\)).
• \(-9\) and \(5\) are constants. Add them by combining their coefficients, -9 and 5, which results in -4.

Understanding how to manipulate coefficients by addition or subtraction is crucial in simplifying polynomial expressions effectively.