91Ó°ÊÓ

Simplifying expressions is a crucial skill in algebra. It involves reducing expressions to their simplest form while keeping the expressions equivalent.
In the given exercise, we start with the expression \[ 4(6x - 1) - (-8) \].
First, we apply the Distributive Property to eliminate the parentheses. This property states that \[ a(b + c) = ab + ac \].
So, we distribute 4 to both terms inside the parentheses, giving us:
\[ 4 \times 6x + 4 \times (-1) \].
This simplifies to:
\[ 24x - 4 \].
Next, we need to handle the negative number outside the parentheses. Subtracting \(-8\) is the same as adding \(8\), so the expression turns into:
\[ 24x - 4 + 8 \].
After distributing and addressing the negative number, we can proceed to our next step: combining like terms.

Combining like terms helps in further simplifying expressions.
Like terms are terms that contain the same variables raised to the same power, though they can have different coefficients.
In our example, after distributing and handling the negative, we have \[ 24x - 4 + 8 \].
To combine like terms, we identify terms that have the same variable form.
In this case, \[24x\] is a term with the variable 'x', while \(-4\) and \(8\) are constant terms.
We combine the constant terms:
\(-4 + 8\), which simplifies to \(4\).
After combining, our final simplified expression is:
\[ 24x + 4 \].
It's essential to correctly identify and combine like terms to ensure that the expression is reduced to its simplest form.

Working with negative numbers can be tricky, but understanding a few basic rules can simplify the process.
In our exercise, we encountered a negative number: \(-8\).
Subtracting a negative number is equivalent to adding its positive value:
\[ a - (-b) = a + b \].
So in the expression \[ 24x - 4 - (-8) \], the subtraction of \(-8\) becomes an addition of \(8\):
\[ 24x - 4 + 8 \].
We then combined the constant terms to make our expression simpler.
Understanding how to handle negative numbers correctly ensures accurate simplification.