Simplify (x+y)7+m: Applying the Distributive Property

Q: Why doesn't the 7 multiply with the m?

The 7 only multiplies what's inside the parentheses (x+y). The term m is added to the product, not multiplied by 7. Think of it as: multiply first, then add.

Q: How do I know when to use the distributive property?

Look for a number or variable directly next to parentheses with no operation sign between them. This means multiplication, so you can distribute!

Q: What if the expression was (x+y+m)7 instead?

Then you would distribute the 7 to all terms: 7x + 7y + 7m. The parentheses determine what gets multiplied by 7.

Q: Is there a difference between (x+y)7 and 7(x+y)?

No difference! Both mean the same thing due to the commutative property of multiplication. You can write multiplication in either order.

Distributive Property with Mixed Terms

It is possible to use the distributive property to simplify the expression

$(x+y)7+m$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Open parentheses properly, multiply by each factor

00:12 Calculate the multiplications

00:17 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

It is possible to use the distributive property to simplify the expression

$(x+y)7+m$

Step-by-step solution

To solve the problem, we first examine whether the distributive property can be applied to the expression $(x+y)7+m$ .

The expression $(x+y)7$ involves multiplying the sum of $x$ and $y$ by 7.
According to the distributive property, we can write this as $7x + 7y$ .
Therefore, the expression simplifies to $7x + 7y + m$ .
Note that the term $m$ is separate and does not involve multiplication; it remains as an addition to the other terms.

Thus, the correct simplified form is $7x + 7y + m$ .

Checking the multiple-choice options, the correct choice is:

No, $7x + 7y + m$

Final Answer

No, $7x+7y+m$

Key Points to Remember

Essential concepts to master this topic

Rule: Apply distributive property only to terms that are multiplied together
Technique: (x+y)7 becomes 7x + 7y, then add separate term m
Check: Verify 7x + 7y + m has no further multiplication to distribute ✓

Common Mistakes

Avoid these frequent errors

Distributing the 7 to the term m incorrectly
Don't distribute 7 to every term in the expression = 7x + 7y + 7m! The term m is added separately, not multiplied by 7. Always identify which terms are multiplied together before applying the distributive property.

Practice Quiz

Test your knowledge with interactive questions

$(3+20)\times(12+4)=$

FAQ

Everything you need to know about this question

Why doesn't the 7 multiply with the m?

The 7 only multiplies what's inside the parentheses (x+y). The term m is added to the product, not multiplied by 7. Think of it as: multiply first, then add.

How do I know when to use the distributive property?

Look for a number or variable directly next to parentheses with no operation sign between them. This means multiplication, so you can distribute!

Can I simplify 7x + 7y + m any further?

No, this is fully simplified! You can't combine terms with different variables (x, y, and the constant m), so this is your final answer.

What if the expression was (x+y+m)7 instead?

Then you would distribute the 7 to all terms: 7x + 7y + 7m. The parentheses determine what gets multiplied by 7.

Is there a difference between (x+y)7 and 7(x+y)?

No difference! Both mean the same thing due to the commutative property of multiplication. You can write multiplication in either order.

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