91Ó°ÊÓ

In algebra, 'like terms' are terms that have the same variable raised to the same power. This means they can be combined because they essentially represent the same quantity, just with different coefficients. For instance, in the expression \-6x - x - 2x\, all terms are like terms because they all contain the variable \(x\).
Even though the coefficients \(the numbers in front of the variables\) are different, the variable itself is the same.
Combining like terms makes an algebraic expression simpler and easier to work with.
Examples of like terms:

• \(3a\) and \(-4a\) (both contain \(a\))
• \(5b^2\) and \(-2b^2\) (both contain \(b^2\))

To sum up, always look at the variable and its exponent behind the coefficient to determine if terms are 'like terms'.

Coefficients are the numerical part of terms in algebraic expressions. In \(4y\), the coefficient is \(4\) and in \(-3z\), the coefficient is \(-3\).
They tell you how many units of the variable you have.
When you combine like terms, you perform operations on the coefficients while keeping the variable part the same.
For instance, in the expression \( -6x - x - 2x\), you simply add the numerical coefficients: \(-6, -1, and -2\). This gives you the sum of \(-9\).
The term then becomes \(-9x\).
Here are some quick points on coefficients:

• The sign of the coefficient (positive or negative) is very important.
• If no coefficient is written, it is understood to be \(1\) (as in \(x\) is actually \(1x\)).

Simplifying an expression means making it as simple as possible.
This can involve combining like terms, reducing fractions, or even factoring.
The goal is to create an expression that is easier to understand and work with.
In our example \(-6x - x - 2x\), simplifying involves combining like terms by adding the coefficients:
\-6 + (-1) + (-2) = -9\.
Therefore, the simplified expression is \(-9x\).
Simplifying expressions is particularly useful when solving equations or performing algebraic manipulations. Here are some guidelines to help simplify algebraic expressions:

• Always combine like terms first.
• Watch out for signs when adding or subtracting coefficients.
• Rewrite the expression in its simplest form for clarity.

Simplifying expressions helps reduce complexity and makes it easier to solve equations later on.
So, whenever you see a long or complicated expression, look for ways to simplify it!