Simplify the Expression: 35m+9n-48m+52n Using Like Terms

Q: What are like terms exactly?

Like terms have identical variables raised to the same powers. In $ 35m + 9n - 48m + 52n $, the m terms (35m and -48m) are like terms, and the n terms (9n and 52n) are like terms.

Q: Why can't I combine 35m and 9n?

Because they have different variables! You can only combine terms with the exact same variable part. Think of it like apples and oranges - you can't add 35 apples to 9 oranges and get 44 "appleoranges".

Q: Does the order of terms matter in my final answer?

No! $ 61n - 13m $ and $ -13m + 61n $ are equivalent. However, it's conventional to write terms in alphabetical order by variable when possible.

Q: How do I handle negative coefficients when combining?

Treat them like regular subtraction: $ 35m - 48m = 35m + (-48m) = (35 + (-48))m = -13m $. The negative sign stays with the coefficient!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify the expression

00:03 Mark the appropriate variables

00:08 Use the commutative law and group equal variables together

00:20 Collect like terms

00:30 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$35m+9n-48m+52n=?$

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Identify and group like terms within the expression.
Combine the coefficients of these like terms.
Simplify the expression by adding or subtracting coefficients.

Now, let's work through each step:

Step 1: Observe the given algebraic expression:
$35m + 9n - 48m + 52n$ .

Step 2: Group like terms, separating terms with $m$ from those with $n$ :
$(35m - 48m)$ and $(9n + 52n)$ .

Step 3: Combine the terms with $m$ :
$35m - 48m = (35 - 48)m = -13m$ .

Step 4: Combine the terms with $n$ :
$9n + 52n = (9 + 52)n = 61n$ .

Therefore, the simplified form of the expression is:
$61n - 13m$ .

This leads to our final solution:

$61n - 13m$

3

Final Answer

$61n-13m$

Key Points to Remember

Essential concepts to master this topic

Identification: Group terms with same variables together before combining
Technique: Add/subtract coefficients: 35m - 48m = (35 - 48)m = -13m
Check: Verify by expanding result: -13m + 61n = 35m + 9n - 48m + 52n ✓

Common Mistakes

Avoid these frequent errors

Combining unlike terms
Don't add m terms to n terms like 35m + 9n = 44mn! Variables must match exactly to combine. Always group same variables: m terms with m terms, n terms with n terms.

Practice Quiz

Test your knowledge with interactive questions

$3x+4x+7+2=\text{?}$

FAQ

Everything you need to know about this question

What are like terms exactly?

+

Like terms have identical variables raised to the same powers. In $35m + 9n - 48m + 52n$ , the m terms (35m and -48m) are like terms, and the n terms (9n and 52n) are like terms.

Why can't I combine 35m and 9n?

+

Because they have different variables! You can only combine terms with the exact same variable part. Think of it like apples and oranges - you can't add 35 apples to 9 oranges and get 44 "appleoranges".

Does the order of terms matter in my final answer?

+

No! $61n - 13m$ and $-13m + 61n$ are equivalent. However, it's conventional to write terms in alphabetical order by variable when possible.

How do I handle negative coefficients when combining?

+

Treat them like regular subtraction: $35m - 48m = 35m + (-48m) = (35 + (-48))m = -13m$ . The negative sign stays with the coefficient!

What if I get zero when combining like terms?

+

If coefficients cancel out completely (like 5x - 5x = 0x), that term disappears from your final answer. This is perfectly normal and means those terms balanced out!

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Simplify the Expression: 35m+9n-48m+52n Using Like Terms

Algebraic Simplification with Like Terms

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