Subtraction of Binomials

Subtracting binomials involves adding the additive inverse of the second binomial to the first. It requires changing the signs of the terms of the binomial being subtracted and then combining the like terms. There are three components of a binomial: 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 binomials, students should follow these rules: Flip signs: Always flip the signs of each term of the second binomial 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, there will be unlike terms remaining. Write the remaining unlike terms as they are, along with the like terms, to get the final result.

The following are the methods of subtraction of binomials: Method 1: Horizontal Method To apply the horizontal method for subtraction of binomials, use the following steps. Step 1: Write both binomials in the same line using a minus sign in between. Step 2: Remove the brackets and change the signs of the second binomial. Step 3: Combine the like terms. Let’s apply these steps to an example: Question: Subtract (4x + 3) from (6x - 5) Step 1: Write both binomials in the same line, (6x - 5) - (4x + 3) Step 2: Remove the brackets and change the signs of the second binomial 6x - 5 - 4x - 3 Step 3: Combine like terms: 2x - 8 Answer: 2x - 8 Method 2: Column Method When subtracting the binomials using the column method, we write the binomials one below the other. Make sure like terms are aligned in each column. Then change the signs of the second binomial and add the binomials. For example, Subtract (2x + 7) from (5x - 1) Solution: Arrange the like terms vertically in columns   5x   +  (-1)   ← Minuend (from which we subtract) - 2x   -  7   ← Subtrahend (what we subtract) -----------------------   3x    -  8 Therefore, upon subtracting, we get 3x - 8

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 a binomial 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 a binomial leaves the binomial as is Subtracting zero from any binomial results in the same binomial: A - 0 = A

Tips and tricks are useful for students to efficiently deal with the subtraction of binomials. Some helpful tips are listed below: Tip 1: Always pay attention to signs before combining like terms. Tip 2: If two binomials have identical terms, cross them out before starting the subtraction. This makes the binomials 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.