Expand the Expression: 8x(5+y) Using Distributive Property

Q: Why do I need to multiply 8x by both 5 and y?

The distributive property says you must multiply the outside term by every term inside the parentheses. Think of it like sharing: if you have 8x groups and each group contains (5 + y), you need 8x × 5 plus 8x × y.

Q: What's the difference between 8xy and 8x + y?

$ 8xy $ means 8 times x times y (multiplication), while $ 8x + y $ means 8 times x plus y (addition). These are completely different expressions!

Q: Can I distribute in any order?

Yes! You can distribute $ 8x $ to the 5 first or to the y first. Either way: $ 8x \cdot 5 + 8x \cdot y = 40x + 8xy $.

Q: How can I check if my answer is right?

Try factoring your answer back! If you get $ 40x + 8xy $, factor out $ 8x $: $ 8x(5 + y) $. This should match your original expression!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:03 We'll open parentheses properly

00:06 We'll make sure the outer term multiplies each of the terms

00:14 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$8x(5+y)=$

2

Step-by-step solution

To solve this problem, we will simplify the expression $8x(5+y)$ using the distributive property.

Step 1: Recognize the expression as $8x$ multiplied by two terms inside a parenthesis, $5$ and $y$ .
Step 2: Apply the distributive property: $8x(5+y) = 8x \cdot 5 + 8x \cdot y$ .
Step 3: Compute each multiplication:
- $8x \cdot 5 = 40x$
- $8x \cdot y = 8xy$
Step 4: Combine the results from the multiplication steps: $40x + 8xy$ .

Thus, the simplified expression of $8x(5+y)$ is $40x + 8xy$ .

Comparing with provided answer choices, the correct solution corresponds to choice $1: 40x + 8xy$ .

3

Final Answer

$40x+8xy$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply outside term by each term inside parentheses
Technique: $8x \cdot 5 = 40x$ and $8x \cdot y = 8xy$
Check: Factor out common term: $40x + 8xy = 8x(5 + y)$ ✓

Common Mistakes

Avoid these frequent errors

Only distributing to the first term
Don't multiply $8x$ by just the 5 to get $40x + y$ ! This ignores the y term completely and violates the distributive property. Always multiply the outside term by every single term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

$12:(2\times2)=$

FAQ

Everything you need to know about this question

Why do I need to multiply 8x by both 5 and y?

+

The distributive property says you must multiply the outside term by every term inside the parentheses. Think of it like sharing: if you have 8x groups and each group contains (5 + y), you need 8x × 5 plus 8x × y.

How do I multiply 8x by y?

+

When multiplying variables, simply write them next to each other: $8x \cdot y = 8xy$ . The coefficient 8 stays in front, and the variables x and y are written together.

What's the difference between 8xy and 8x + y?

+

$8xy$ means 8 times x times y (multiplication), while $8x + y$ means 8 times x plus y (addition). These are completely different expressions!

Can I distribute in any order?

+

Yes! You can distribute $8x$ to the 5 first or to the y first. Either way: $8x \cdot 5 + 8x \cdot y = 40x + 8xy$ .

How can I check if my answer is right?

+

Try factoring your answer back! If you get $40x + 8xy$ , factor out $8x$ : $8x(5 + y)$ . This should match your original expression!

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Expand the Expression: 8x(5+y) Using Distributive Property

Distributive Property with Algebraic Terms

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Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I need to multiply 8x by both 5 and y?

How do I multiply 8x by y?

What's the difference between 8xy and 8x + y?

Can I distribute in any order?

How can I check if my answer is right?

🌟 Unlock Your Math Potential

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