Question
Add and .
Solution — Step by Step
Place the two expressions side by side with a plus sign between them:
We keep the brackets only for clarity — they don’t change anything here since we’re adding.
Like terms share the same variable (and the same power of that variable). Here:
- -terms: and
- -terms: and
Constants would form their own group, but we don’t have any here.
We’re essentially using the distributive law in reverse — factoring out the .
Remember, means , so the coefficient is , not zero.
That’s the final answer. Nothing more to simplify — and are unlike terms.
Why This Works
In algebra, a “term” is a product of a number and variables. The number part is called the coefficient. When two terms have identical variable parts — same letters, same powers — they are “like terms” and their coefficients can simply be added or subtracted.
Think of it this way: means “3 bags of ” and means “5 bags of .” Together, that’s 8 bags of . But you can’t add bags of to bags of — they’re different things. This is exactly why cannot be simplified further.
This concept is the foundation of almost every algebraic manipulation you’ll do in Class 7, 8, and beyond — factoring, solving equations, polynomial addition. Get comfortable with spotting like terms quickly.
Alternative Method
Column method — arrange like terms in columns before adding. This is especially useful when you have three or more expressions.
Write like terms in the same column, then add each column. Many students find this cleaner when the expressions get longer (four or five terms each). NCERT exercises often use this format in the worked examples.
Common Mistake
Dropping the negative sign on .
Students write instead of . The second expression is , which means the -term has a coefficient of . When you collect it, you must carry that minus sign with it.
Always rewrite as in your rough work until sign handling becomes automatic.
Quick check: Substitute a simple value like into both the original expression and your answer. Original: . Answer: . Match — you’re good.
This substitution trick takes 10 seconds and will catch most sign errors before they cost you marks.