Equivalent Forms: Expanding (5+1)×(500+30+2) Factor Expression

Q: Why can't I just add all the numbers together?

Because the parentheses and multiplication sign tell you the structure! $ (5+1)\times(500+30+2) $ means "find two sums, then multiply them," not "add everything up."

Q: Do I have to solve both parentheses completely?

Yes! You must calculate $ 5+1=6 $ and $ 500+30+2=532 $ separately before multiplying. This gives you $ 6\times532 $.

Q: What if I get confused about which operation to do first?

Remember PEMDAS! Parentheses come first, so solve everything inside ( ) before doing any multiplication. Think of parentheses as "solve me first" boxes.

Q: How do I know 532 is correct for the second parentheses?

Add step by step: $ 500+30=530 $, then $ 530+2=532 $. You can also verify: 5 hundreds + 3 tens + 2 ones = 532.

Q: Is there a faster way to solve this?

Once you understand the concept, you can recognize that $ (5+1) $ and $ (500+30+2) $ are just expanded forms of 6 and 532. But always show your work!

Factored Expressions with Parenthetical Addition

Which equation is the same as the following factored equation?

$(5+1)\times(500+30+2)$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the expression that represents the correct solution of the exercise

00:03 Let's solve what's inside the parentheses

00:12 Let's solve one addition operation at a time

00:26 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

Which equation is the same as the following factored equation?

$(5+1)\times(500+30+2)$

Step-by-step solution

Given that we have two exercises in parentheses, we know that each of them represents a number.

Therefore, what we will do is solve the exercises in parentheses to reveal which two numbers we are multiplying:

$5+1=6$

$500+30=530+2=532$

Now we get the exercise:

$6\times532$

Final Answer

$6\times532$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Solve expressions inside parentheses first
Technique: Calculate (5+1)=6 and (500+30+2)=532 separately
Check: Verify 6×532 equals original expression result ✓

Common Mistakes

Avoid these frequent errors

Adding all numbers together instead of following parentheses
Don't calculate 5+1+500+30+2 = 538! This ignores the multiplication structure and gives completely wrong results. Always solve parentheses first, then multiply the results together.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why can't I just add all the numbers together?

Because the parentheses and multiplication sign tell you the structure! $(5+1)\times(500+30+2)$ means "find two sums, then multiply them," not "add everything up."

Do I have to solve both parentheses completely?

Yes! You must calculate $5+1=6$ and $500+30+2=532$ separately before multiplying. This gives you $6\times532$ .

What if I get confused about which operation to do first?

Remember PEMDAS! Parentheses come first, so solve everything inside ( ) before doing any multiplication. Think of parentheses as "solve me first" boxes.

How do I know 532 is correct for the second parentheses?

Add step by step: $500+30=530$ , then $530+2=532$ . You can also verify: 5 hundreds + 3 tens + 2 ones = 532.

Is there a faster way to solve this?

Once you understand the concept, you can recognize that $(5+1)$ and $(500+30+2)$ are just expanded forms of 6 and 532. But always show your work!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Commutative, Distributive and Associative Properties questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime