Simplify the Expression: xy - 3x² + 2y² - 6x²

Q: What makes terms 'like terms'?

Like terms have exactly the same variables raised to the same powers. For example: $ 3x^2 $ and $ -6x^2 $ are like terms, but $ xy $ and $ x^2 $ are not!

Q: Why can't I combine xy with x² terms?

Because $ xy $ means 'x times y' while $ x^2 $ means 'x times x' - they're completely different mathematical objects! Only combine terms that have identical variable parts.

Q: How do I add the coefficients of like terms?

Just add or subtract the numbers in front of the variables! For $ -3x^2 - 6x^2 $, calculate $ -3 + (-6) = -9 $, so you get $ -9x^2 $.

Q: What if there's no coefficient written?

When no number is written, the coefficient is 1! So $ xy $ actually means $ 1xy $, and you can treat it as having coefficient 1 when combining terms.

Q: How should I arrange my final answer?

Write terms in descending order of powers or alphabetically by variables. So $ xy - 9x^2 + 2y^2 $ could be rewritten as $ -9x^2 + xy + 2y^2 $ for better organization.

Algebraic Simplification with Like Terms

$x\times y-3x\times x+2y\times y-6x^2=$

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Step-by-step video solution

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00:00 Simply

00:03 Let's calculate the multiplications

00:18 Let's gather the factors

00:29 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

$x\times y-3x\times x+2y\times y-6x^2=$

Step-by-step solution

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

Step 1: Identify like terms.
Step 2: Simplify the expression by combining like terms.

Let's simplify the given expression:
The expression is given as $x \times y - 3x \times x + 2y \times y - 6x^2$ .

First, simplify each term:
- $x \times y$ remains $xy$ .
- $3x \times x$ simplifies to $3x^2$ .
- So, the expression becomes $xy - 3x^2 + 2y^2 - 6x^2$ .

Next, combine like terms:
- Combine the $x^2$ terms: $-3x^2 - 6x^2 = -9x^2$ .
- The $xy$ term and $2y^2$ term are unique and remain as they are.

This results in the simplified expression: $xy - 9x^2 + 2y^2$ .

Upon comparing this simplification with the answer choices, the correct option is:

$xy - 9x^2 + 2y^2$

Therefore, the solution to the problem is $xy - 9x^2 + 2y^2$ .

Final Answer

$xy-9x^2+2y^2$

Key Points to Remember

Essential concepts to master this topic

Rule: Identify like terms by matching variables and their powers
Technique: Combine $-3x^2 - 6x^2 = -9x^2$ by adding coefficients
Check: Each variable type appears only once in final answer ✓

Common Mistakes

Avoid these frequent errors

Combining unlike terms together
Don't add xy + x² = 2x³ or similar nonsense = completely wrong answer! Different variable combinations cannot be combined because they represent different mathematical quantities. Always group only terms with identical variable parts and powers.

Practice Quiz

Test your knowledge with interactive questions

Are the expressions the same or not?

$$ 20x $$

$2\times10x$

FAQ

Everything you need to know about this question

What makes terms 'like terms'?

Like terms have exactly the same variables raised to the same powers. For example: $3x^2$ and $-6x^2$ are like terms, but $xy$ and $x^2$ are not!

Why can't I combine xy with x² terms?

Because $xy$ means 'x times y' while $x^2$ means 'x times x' - they're completely different mathematical objects! Only combine terms that have identical variable parts.

How do I add the coefficients of like terms?

Just add or subtract the numbers in front of the variables! For $-3x^2 - 6x^2$ , calculate $-3 + (-6) = -9$ , so you get $-9x^2$ .

What if there's no coefficient written?

When no number is written, the coefficient is 1! So $xy$ actually means $1xy$ , and you can treat it as having coefficient 1 when combining terms.

How should I arrange my final answer?

Write terms in descending order of powers or alphabetically by variables. So $xy - 9x^2 + 2y^2$ could be rewritten as $-9x^2 + xy + 2y^2$ for better organization.

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