Simplify the Expression: 5.6x + 7.9y + 53xy + 12.1x

Q: Why can't I combine x and xy terms together?

Because x and xy are different variable types! Think of x as 'apples' and xy as 'apple pies' - you can't add them together. Only combine terms with exactly the same variables and powers.

Q: What's the difference between 53xy and 53x + 53y?

$ 53xy $ means 53 times x times y, while $ 53x + 53y $ means 53 times x plus 53 times y. These are completely different expressions that cannot be combined!

Q: Do I need to put the terms in a specific order?

No specific order is required, but it's good practice to write terms in alphabetical order by variable: x terms first, then xy terms, then y terms. This makes your answer easier to read.

Q: How do I know which terms are 'like terms'?

Like terms have exactly the same variable part. For example: $ 5.6x $ and $ 12.1x $ both have just 'x', so they're like terms. But $ x $ and $ xy $ are different!

Q: What if I have decimal coefficients like 5.6 and 12.1?

Treat decimal coefficients just like whole numbers! Simply add them together: $ 5.6 + 12.1 = 17.7 $. The variable part stays exactly the same.

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

00:09 Use the commutative law and arrange the appropriate variables together

00:27 Collect like terms

00:36 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

^{$5.6x+7.9y+53xy+12.1x=\text{?}$}

2

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Identify Like Terms

The expression is $5.6x + 7.9y + 53xy + 12.1x$ . Here, $5.6x$ and $12.1x$ are like terms.

Step 2: Combine Like Terms

Add the coefficients of $x$ : $5.6x + 12.1x = (5.6 + 12.1)x = 17.7x$ .

Step 3: Write the Simplified Expression

After combining the like terms, we get:

$17.7x + 7.9y + 53xy$

This is the simplified form of the expression.

Therefore, the solution to the problem is $17.7x + 53xy + 7.9y$ .

3

Final Answer

_{^{$17.7x+53xy+7.9y$}}

Key Points to Remember

Essential concepts to master this topic

Identification: Find terms with identical variable parts and same powers
Technique: Add coefficients only: 5.6x + 12.1x = (5.6 + 12.1)x = 17.7x
Check: Count terms before and after: 4 terms become 3 terms ✓

Common Mistakes

Avoid these frequent errors

Combining terms with different variables or powers
Don't combine 5.6x + 7.9y = 13.5xy or add xy terms to x terms! Different variables cannot be combined - they're like adding apples to oranges. Always combine 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

Why can't I combine x and xy terms together?

+

Because x and xy are different variable types! Think of x as 'apples' and xy as 'apple pies' - you can't add them together. Only combine terms with exactly the same variables and powers.

What's the difference between 53xy and 53x + 53y?

+

$53xy$ means 53 times x times y, while $53x + 53y$ means 53 times x plus 53 times y. These are completely different expressions that cannot be combined!

Do I need to put the terms in a specific order?

+

No specific order is required, but it's good practice to write terms in alphabetical order by variable: x terms first, then xy terms, then y terms. This makes your answer easier to read.

How do I know which terms are 'like terms'?

+

Like terms have exactly the same variable part. For example: $5.6x$ and $12.1x$ both have just 'x', so they're like terms. But $x$ and $xy$ are different!

What if I have decimal coefficients like 5.6 and 12.1?

+

Treat decimal coefficients just like whole numbers! Simply add them together: $5.6 + 12.1 = 17.7$ . The variable part stays exactly the same.

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Simplify the Expression: 5.6x + 7.9y + 53xy + 12.1x

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