Subtraction of Variables

Subtracting variables involves adding the additive inverse of the second expression to the first. It requires changing the signs of the terms of the expression being subtracted and then combining like terms.

There are three components involved:

Coefficients: These are constant values like -1, 4, etc.

Variables: These are unknown quantities like x, y, z, etc.

Operators: For subtraction, the operator is the minus (-) symbol.

When subtracting variables, students should follow these steps:

Flip signs: Always flip the signs of each term in the second expression and perform addition.

Combine like terms: Only like terms can be subtracted from one another, so group all like terms together.

Simplifying result: After all like terms are combined, write the remaining unlike terms as they are, along with the like terms, to get the final result.

The following are methods for subtraction of variables:

Method 1: Horizontal Method

To apply the horizontal method for subtraction of variables, follow these steps:

Step 1: Write both expressions in the same line using a minus sign in between.

Step 2: Remove the brackets and change the signs of the second expression.

Step 3: Combine the like terms.

Let’s apply these steps to an example: Question: Subtract 8a - 3b from 14a + 5b

Step 1: Write both expressions in the same line as (14a + 5b) - (8a - 3b).

Step 2: Remove the brackets and change the signs of the second expression: 14a + 5b - 8a + 3b.

Step 3: Write like terms together: 6a + 8b. Answer: 6a + 8b

Method 2: Column Method

When subtracting variables using the column method, write the expressions one below the other, ensuring like terms are aligned in each column. Then change the signs of the second expression and add the expressions.

For example, Subtract 9x + 7 from 5x - 2

Solution: Arrange the like terms vertically in columns 5x - 2 ← Minuend (from which we subtract) - 9x - 7 ← Subtrahend (what we subtract) ----------------------- -4x + 5

Therefore, upon subtracting, we get -4x + 5

In algebra, subtraction has some characteristic properties. These properties are listed below:

• Subtraction is not commutative In subtraction, changing the order of the terms changes the result, i.e., A - B ≠ B - A

• Subtraction is not associative Unlike addition, we cannot regroup in subtraction. When three or more expressions are involved, changing the grouping changes the result. (A − B) − C ≠ A − (B − C)

• Subtraction is the addition of the opposite sign Subtracting an expression is the same as adding its opposite, so to make calculations easier, you can convert subtraction into addition by changing the signs of the second term. A − B = A + (−B)

• Subtracting zero from an expression leaves the expression as is Subtracting zero from any expression results in the same algebraic expression: A - 0 = A

Tips and tricks are useful for students to efficiently deal with the subtraction of variables. Some helpful tips are listed below:

Tip 1: Always pay attention to signs before combining like terms.

Tip 2: If two expressions have identical terms, cross them out before starting the subtraction. This makes the expressions shorter and provides more clarity due to fewer terms.

Tip 3: Beginners and visual learners can benefit from using the box model or column method to avoid missing signs and mismatching terms.

Subtraction in algebra is comparatively more challenging than addition, often leading to common mistakes. However, being aware of these errors can help students avoid them.