91Ó°ÊÓ

In algebraic expressions, combining like terms is a crucial operation. Like terms are terms that have the exact same variable raised to the same power. Here's how you can spot them using the example expression provided:

• Terms containing the variable \( x \) are like terms. In this case, \( 5.7x \) and \( -6.2x \) are like terms because they both involve the variable \( x \).
• Similarly, terms with \( y \) are also like terms. For instance, \( 9.4y \) and \( -4.4y \) share the same variable \( y \).

Once identified, combine these terms by adding or subtracting their coefficients. This simplifies the total number of terms in your expression, making it more manageable and easier to understand.

Simplifying expressions involves reducing them to their simplest form. This often means combining like terms and consolidating the expression into fewer, more understandable terms.
To simplify, start by:

• Identifying like terms, such as those with the same variables (e.g., \( x \) or \( y \)).
• Combining these like terms by adding or subtracting their coefficients. For example, for the term \( 5.7x - 6.2x \), compute \((5.7 - 6.2) = -0.5\) and multiply the result by \( x \); yielding \( -0.5x \).
• Doing similar operations for other like terms, such as \( 9.4y - 4.4y \), which simplifies to \(5y\).

After combining all possible like terms, your algebraic expression will be in its simplest form, presenting a clear, concise result that is often necessary for solving equations or understanding algebraic relationships.

Coefficients are the numerical parts of terms in an algebraic expression. When combining like terms, it's important to focus on these coefficients, as they are what add or subtract from each other.
In our original problem, the terms \( 5.7x \), \( -6.2x \), \( 9.4y \), and \( -4.4y \) each have coefficients:

• 5.7 attached to the variable \( x \)
• -6.2 also attached to \( x \)
• 9.4 with the variable \( y \)
• -4.4 with \( y \)

When we combine like terms, we perform operations on these coefficients. For instance, adding the coefficients of \( x \) means calculating \( 5.7 + (-6.2) \), resulting in \( -0.5 \), which becomes the new coefficient of \( x \).
Similarly, the coefficients of \( y \) combine as \( 9.4 + (-4.4) \) to yield \( 5 \). Understanding coefficients and their manipulation is key to mastering algebraic expressions.