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The distributive property is a fundamental building block in algebra. It's like a magic tool that allows you to simplify expressions easily by breaking them down and getting rid of parentheses. Here, we focus on how this property works when subtracting quantities wrapped inside parentheses.
A common situation where this is used is with subtraction involving binomials, for example,

• \((a-5)-(-3a+2)\)

To tackle this, you distribute the negative sign to both terms inside the parentheses. Think of the negative sign as multiplying by

• -1, so
  • \(-( -3a + 2)\)
  • becomes \(+3a - 2\).

By distributing the negative sign across the terms in the parentheses, you simplify the expression for further operations. It's an essential skill for solving algebraic expressions effectively.

Combining like terms is another crucial step in simplifying algebraic expressions. This process involves grouping together terms that have the same variable raised to the same power. Basically, they are the terms that "look alike."
Consider the expression we are working with:

• \((a - 5) + (3a - 2)\)

Here, you have two types of terms:

• terms involving \(a\), and
• constant numbers.

To combine like terms:

• Add the coefficients of terms involving \(a\), so \(a + 3a = 4a\).
• Add the constants: \(-5 - 2 = -7\).

By combining these like terms, you slowly transform the expression into a more manageable form.

Simplifying expressions is the ultimate goal in algebra to make your results easy to understand and work with. After you have used the distributive property and combined like terms, you should have an expression like:

• \(4a - 7\)

This expression is as simplified as it can be because all like terms have been combined and no further operations are possible. Simplification is important because:

• it makes algebraic expressions easier to interpret;
• it prepares equations for further operations such as solving or setting equal to other expressions.

When you simplify an expression, you are essentially finding a clearer way to express a mathematical idea, ready for more complex calculations or analyses.