Find the Equivalent Expression: 3×(20+3)×(20+5)

Q: Why can't I just distribute the 3 to everything?

The distributive property only works when you have multiplication over addition, like $ a(b+c) $. Here we have three separate factors being multiplied together, so solve parentheses first!

Q: What's the difference between this and 3×(20+3+20+5)?

Huge difference! Your expression has two separate parentheses that are multiplied together. The other has one set of parentheses with all terms added inside. Always pay attention to grouping symbols!

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

Yes! You can use the commutative property to rearrange: $ (20+3) \times 3 \times (20+5) $ or $ (20+5) \times (20+3) \times 3 $. Just solve parentheses first in any order!

Q: How do I know which answer choice is equivalent?

Simplify the original expression step by step: solve $ (20+3) = 23 $ and $ (20+5) = 25 $. Then look for $ 3 \times 23 \times 25 $ among the choices.

Q: What if I made a calculation error in the parentheses?

Double-check your arithmetic! $ 20 + 3 = 23 $ and $ 20 + 5 = 25 $. A small error here will make all answer choices look wrong, so verify these basic additions first.

Order of Operations with Parenthetical Expressions

Which equation is the same as the following?

$3\times(20+3)\times(20+5)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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

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

00:14 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?

$3\times(20+3)\times(20+5)$

Step-by-step solution

Let's consider that each set of parentheses represents a number.

That is, if we solve the exercises within the parentheses, we will get a multiplication exercise of three numbers. We can't simplify the 3 so it does not get factored.

We solve each of the exercises within the parentheses to reveal what the numbers are:

$20+3=23$

$20+5=25$

That is, the exercise we obtained is the multiplication between three numbers:

$3\times23\times25$

Final Answer

$3\times23\times25$

Key Points to Remember

Essential concepts to master this topic

Rule: Solve parentheses first before multiplying the results together
Technique: Calculate (20+3)=23 and (20+5)=25, then multiply 3×23×25
Check: Original expression and simplified form give same result: 1725 ✓

Common Mistakes

Avoid these frequent errors

Incorrectly distributing multiplication across addition
Don't change 3×(20+3)×(20+5) to 3×20+3×20+5 = wrong structure! This breaks the grouping and ignores proper order of operations. Always solve what's inside parentheses first, then multiply the results.

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 3 to everything?

The distributive property only works when you have multiplication over addition, like $a(b+c)$ . Here we have three separate factors being multiplied together, so solve parentheses first!

What's the difference between this and 3×(20+3+20+5)?

Huge difference! Your expression has two separate parentheses that are multiplied together. The other has one set of parentheses with all terms added inside. Always pay attention to grouping symbols!

Can I solve this problem in a different order?

Yes! You can use the commutative property to rearrange: $(20+3) \times 3 \times (20+5)$ or $(20+5) \times (20+3) \times 3$ . Just solve parentheses first in any order!

How do I know which answer choice is equivalent?

Simplify the original expression step by step: solve $(20+3) = 23$ and $(20+5) = 25$ . Then look for $3 \times 23 \times 25$ among the choices.

What if I made a calculation error in the parentheses?

Double-check your arithmetic! $20 + 3 = 23$ and $20 + 5 = 25$ . A small error here will make all answer choices look wrong, so verify these basic additions first.

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