Simplify (-x²) + (-2½x²): Combining Like Terms with Negative Squares

Q: Why do I get a negative answer when adding two negative terms?

When you add two negative numbers, the result is always more negative! Think of it like debt: if you owe $1 and then owe another $2.50, you owe a total of $3.50.

Q: How do I handle the mixed number -2½?

Convert mixed numbers to decimals for easier calculation: -2½ = -2.5. Then add: -1 + (-2.5) = -3.5 = -3½.

Q: What makes these 'like terms' that I can combine?

Both terms have the exact same variable part: x². Like terms have identical variables with identical exponents, so you can add their coefficients together.

Q: Can I write the answer as -3.5x² instead of -3½x²?

Yes! $ -3.5x^2 $ and $ -3\frac{1}{2}x^2 $ are equivalent. Use whichever form matches what your teacher prefers or what the answer choices show.

Q: What if I accidentally made both coefficients positive?

Double-check the original problem! Both terms have negative signs in front: (-x²) and (-2½x²). Missing these signs is the most common mistake in this type of problem.

Combining Like Terms with Mixed Numbers

$(-x^2)+(-2\frac{1}{2}x^2)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify

00:06 Positive times negative always equals negative

00:09 Open parentheses

00:20 The coefficient of any number is always 1

00:28 Collect terms

00:31 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(-x^2)+(-2\frac{1}{2}x^2)=$

Step-by-step solution

To solve the problem, follow these steps:

Step 1: Identify the coefficients of the terms involved.
Step 2: Add the coefficients while considering their signs.
Step 3: Write the simplified expression.

Let's break down the calculation:
Step 1: The expression given is $(-x^2) + (-2\frac{1}{2}x^2)$ .
Step 2: Recognize that $-x^2$ has a coefficient of $-1$ and $-2\frac{1}{2}x^2$ has a coefficient of $-2.5$ .
Step 3: Add these coefficients: $-1 + (-2.5) = -3.5$ .
Therefore, the simplified expression is $-3.5x^2$ .

Thus, the solution to the problem is $-3\frac{1}{2}x^2$ .

Final Answer

$-3\frac{1}{2}x^2$

Key Points to Remember

Essential concepts to master this topic

Rule: Add coefficients of like terms while keeping the variable part
Technique: Convert mixed numbers: -2½ becomes -2.5, then -1 + (-2.5) = -3.5
Check: Verify both terms have x² and coefficients add to -3½ ✓

Common Mistakes

Avoid these frequent errors

Ignoring negative signs when adding coefficients
Don't treat (-x²) + (-2½x²) as just adding 1 + 2½ = 3½! This ignores the negative signs and gives a positive result instead of negative. Always carefully track negative signs: -1 + (-2.5) = -3.5, not +3.5.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

Why do I get a negative answer when adding two negative terms?

When you add two negative numbers, the result is always more negative! Think of it like debt: if you owe $1 and then owe another$ 2.50, you owe a total of $3.50.

How do I handle the mixed number -2½?

Convert mixed numbers to decimals for easier calculation: -2½ = -2.5. Then add: -1 + (-2.5) = -3.5 = -3½.

What makes these 'like terms' that I can combine?

Both terms have the exact same variable part: x². Like terms have identical variables with identical exponents, so you can add their coefficients together.

Can I write the answer as -3.5x² instead of -3½x²?

Yes! $-3.5x^2$ and $-3\frac{1}{2}x^2$ are equivalent. Use whichever form matches what your teacher prefers or what the answer choices show.

What if I accidentally made both coefficients positive?

Double-check the original problem! Both terms have negative signs in front: (-x²) and (-2½x²). Missing these signs is the most common mistake in this type of problem.

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