Algebra : Addition & Subtraction In Sequence
When two algebraic terms are “like” terms, they can be added or subtracted. In this course, you will learn how to simplify expressions without rearranging or grouping terms, even when dealing with more than 10 terms, so you can work through them confidently and accurately.
Related Lessons:
Add/Subtract Algebra Expression Without Rearrangement
One of the most common mistakes students make is rearranging algebraic terms when adding or subtracting. This lesson teaches you how to work confidently by adding and subtracting terms in a clear, step-by-step sequence—without rearranging the expression by simplifying the following expression:
\(3x^2-2x^3-x^4-x^2+x^3-x^4=?\)
- To start off, we will add the highest power \(x^4\) to get \(-2x^4\)
- Next, we add the \(x^3\) term to get \(-x^3\)
- Finally, we add the \(x^2\) term to get \(2x^2\)
- So the final answer is
- \(-2x^4-x^3+2x^2\)
Perform Cancellation Before Add/Subtract
When faced with a large algebraic expression, a quicker method is to perform “cancellations” first before simplifying the terms. This approach helps reduce complexity and makes the simplification process more efficient. There are 3 approaches:
- Simple cancellation, where 2 algebra terms have the same coefficient but different signs, e.g. \(-2x\) and \(2x\)
- Intermediate cancellation, where sum of 2 terms is the negative results of 1 term, e.g. \(-2x-x+5y+3z+3x=5y+3z\) as the \(x\)-terms will cancel out each other
- Advanced cancellation where more than 3 terms will cancel out one term
Three Rules To Remember
Three key rules to remember when adding or subtracting algebra terms:
- Always write algebra in alphabetical order with the numbers in front of the algebra
- When adding or subtracting algebra, never regroup the “Like” terms together before adding/subtracting. It is prone to careless mistakes.
- If possible, arrange the power from the highest to the lowest in your final answer.
Watch Full Concept Breakdown
Developing a strong technique for adding and subtracting algebraic expressions is essential. The video below demonstrates a clear, step-by-step method taught above to perform addition and subtraction without rearranging the terms, minimising careless mistakes and improves accuracy.