Analyze the Expression: 2×(10+2)×(20+2) Decomposition

Q: Why can't I just distribute the 2 to each term in the parentheses?

Because distribution would give you $ 2×10 + 2×2 + 2×20 + 2×2 $, which is completely different! The parentheses here represent complete numbers that need to be calculated first.

Q: What does it mean that parentheses 'represent a number'?

Each set of parentheses contains an addition problem that equals one specific number. $ (10+2) $ represents the number 12, and $ (20+2) $ represents the number 22.

Q: How do I know when to solve parentheses first vs. distribute?

Look at the structure! If you have multiplication between separate parenthetical groups like $ (a+b)×(c+d) $, solve each parentheses first. Distribution works for $ a×(b+c) $.

Q: Can I solve this problem in a different order?

No! The order of operations (PEMDAS) requires you to solve parentheses first. You must calculate what's inside each set of parentheses before doing any multiplication.

Q: What if I get confused about which numbers to multiply?

After solving parentheses, rewrite the expression clearly: $ 2×12×22 $. This shows you're multiplying three separate numbers together.

Expression Evaluation with Parenthetical Addition

Which exercise does the following decomposition represent?

$2\times(10+2)\times(20+2)$

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Step-by-step video solution

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00:00 Find the expression representing the correct factorization of the exercise

00:03 Let's solve what's inside the parentheses to find the expression

00:13 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Which exercise does the following decomposition represent?

$2\times(10+2)\times(20+2)$

Step-by-step solution

Note that all parentheses represent a number for us.

This means that if we solve the expressions in parentheses, we will get an exercise of multiplication between three numbers.

We will leave 2 as it is since it is not a number inside parentheses but stands on its own.

Let's solve each of the expressions in parentheses to discover what the numbers are:

$10+2=12$

$20+2=22$

Therefore, the exercise we got is multiplication between three numbers:

$2\times12\times22$

Final Answer

$2\times12\times22$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Solve expressions inside parentheses first, then multiply
Technique: Calculate (10+2)=12 and (20+2)=22 before multiplying
Check: Final result should be multiplication of three numbers: 2×12×22 ✓

Common Mistakes

Avoid these frequent errors

Distributing multiplication before solving parentheses
Don't multiply 2×10 and 2×20 separately = wrong structure! This changes the expression completely and gives incorrect results. Always solve what's inside parentheses first, then multiply the resulting numbers.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why can't I just distribute the 2 to each term in the parentheses?

Because distribution would give you $2×10 + 2×2 + 2×20 + 2×2$ , which is completely different! The parentheses here represent complete numbers that need to be calculated first.

What does it mean that parentheses 'represent a number'?

Each set of parentheses contains an addition problem that equals one specific number. $(10+2)$ represents the number 12, and $(20+2)$ represents the number 22.

How do I know when to solve parentheses first vs. distribute?

Look at the structure! If you have multiplication between separate parenthetical groups like $(a+b)×(c+d)$ , solve each parentheses first. Distribution works for $a×(b+c)$ .

Can I solve this problem in a different order?

No! The order of operations (PEMDAS) requires you to solve parentheses first. You must calculate what's inside each set of parentheses before doing any multiplication.

What if I get confused about which numbers to multiply?

After solving parentheses, rewrite the expression clearly: $2×12×22$ . This shows you're multiplying three separate numbers together.

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