Find the Equivalent Expression: (30+2)×(10+4) Multiplication

Q: Why can't I just multiply the first numbers together?

Because the parentheses create groups that must be solved first! $ (30+2) $ means "30 plus 2 as one number," not separate terms to distribute.

Q: Is there a shortcut for this type of problem?

No shortcuts needed! Just follow PEMDAS: Parentheses first, then multiplication. It's actually easier than trying to distribute and makes fewer mistakes.

Q: How do I know which numbers to add together?

Look for the parentheses! Everything inside the same set of parentheses gets calculated together: $ (30+2) $ and $ (10+4) $ are separate groups.

Parentheses Operations with Addition Before Multiplication

Which equation is the same as the following?

$(30+2)\times(10+4)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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

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

00:10 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?

$(30+2)\times(10+4)$

Step-by-step solution

Let's keep in mind 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 two numbers.

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

$30+2=32$

$10+4=14$

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

$32\times14$

Final Answer

$32\times14$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Always solve inside parentheses first before multiplying
Technique: Calculate 30+2=32 and 10+4=14, then multiply the results
Check: Verify that 32×14 gives the same result as the original expression ✓

Common Mistakes

Avoid these frequent errors

Distributing multiplication before solving parentheses
Don't multiply 30×10 and 2×4 separately = gets 300+8=308 which is wrong! This ignores the parentheses groupings and violates order of operations. Always solve what's inside each set of parentheses completely first.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why can't I just multiply the first numbers together?

Because the parentheses create groups that must be solved first! $(30+2)$ means "30 plus 2 as one number," not separate terms to distribute.

What if I forget to add inside the parentheses?

You'll get the wrong answer! For example, if you use 30×10=300 instead of 32×14=448, you're off by a lot. Always complete the addition first.

Is there a shortcut for this type of problem?

No shortcuts needed! Just follow PEMDAS: Parentheses first, then multiplication. It's actually easier than trying to distribute and makes fewer mistakes.

How do I know which numbers to add together?

Look for the parentheses! Everything inside the same set of parentheses gets calculated together: $(30+2)$ and $(10+4)$ are separate groups.

What if the parentheses had subtraction instead?

Same rule applies! Solve inside the parentheses first, whether it's addition, subtraction, or any other operation. The parentheses always take priority.

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