Simplify (17+c)(5+a+3): Applying the Distributive Property

Q: Why do I need to simplify (5+a+3) before distributing?

Simplifying first makes the problem much easier! Instead of distributing to three terms, you only distribute to two terms: $ (17+c)(8+a) $.

Q: How do I know which terms to combine inside the parentheses?

Look for like terms - numbers with numbers, variables with the same variables. In $ (5+a+3) $, combine the constants: 5 + 3 = 8.

Q: What's the correct order when using the distributive property?

Follow FOIL method: First terms, Outer terms, Inner terms, Last terms. For $ (17+c)(8+a) $:First: 17 × 8 = 136Outer: 17 × a = 17aInner: c × 8 = 8cLast: c × a = ca

Q: What if there are more than two sets of parentheses?

The same rules apply! Simplify each set of parentheses first, then use the distributive property step by step. Always work from the inside out.

Distributive Property with Algebraic Expressions

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

$(17+c)(5+a+3)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Collect terms

00:09 Open parentheses properly, multiply each term by each term

00:29 Calculate the products

00:44 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

$(17+c)(5+a+3)$

Step-by-step solution

We may use the parenthesis on the right hand side due to the fact that it can be simplified as follows :

(8+a)

Resulting in the following calculation:

$(17+c)(8+a)=$

$136+17a+8c+ca$

Final Answer

Yes, $136+17a+8c+ca$

Key Points to Remember

Essential concepts to master this topic

Simplify First: Combine like terms inside parentheses before distributing
Technique: Transform (17+c)(5+a+3) to (17+c)(8+a) by adding constants
Check: Verify by expanding: 17×8 + 17a + c×8 + ca = 136+17a+8c+ca ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify expressions in parentheses first
Don't distribute (17+c) to each term in (5+a+3) separately = creates unnecessary complexity! This leads to extra terms and calculation errors. Always simplify expressions inside parentheses before applying the distributive property.

Practice Quiz

Test your knowledge with interactive questions

$$ (x+y)(x-y)= $$

FAQ

Everything you need to know about this question

Why do I need to simplify (5+a+3) before distributing?

Simplifying first makes the problem much easier! Instead of distributing to three terms, you only distribute to two terms: $(17+c)(8+a)$ .

How do I know which terms to combine inside the parentheses?

Look for like terms - numbers with numbers, variables with the same variables. In $(5+a+3)$ , combine the constants: 5 + 3 = 8.

What's the correct order when using the distributive property?

Follow FOIL method: First terms, Outer terms, Inner terms, Last terms. For $(17+c)(8+a)$ :

First: 17 × 8 = 136
Outer: 17 × a = 17a
Inner: c × 8 = 8c
Last: c × a = ca

How can I check if my final answer is correct?

Substitute simple values for the variables and verify both expressions give the same result. For example, let a=1 and c=2, then check both $(17+2)(5+1+3)$ and your answer.

What if there are more than two sets of parentheses?

The same rules apply! Simplify each set of parentheses first, then use the distributive property step by step. Always work from the inside out.

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