Simplify the Expression: 14+8a-(7b-13-2a)

Distributive Property with Negative Signs

14+8a(7b132a)=? 14+8a-(7b-13-2a)=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Always solve parentheses first
00:07 Note, negative times positive is always negative
00:11 Note, negative times negative is always positive
00:23 Collect like terms
00:37 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

14+8a(7b132a)=? 14+8a-(7b-13-2a)=\text{?}

2

Step-by-step solution

First, we address the exercise within the parentheses:

Remember that:

When we multiply a positive number by a negative number, the result will be negative.

When we multiply a negative number by a negative number, the result will be positive.

Now we obtain:

14+8a7b+13+2a= 14+8a-7b+13+2a=

We join the coefficients to:

8a+2a=10a 8a+2a=10a

We join the numbers without coefficients:

14+13=27 14+13=27

We obtain:

27+10a7b 27+10a-7b

3

Final Answer

27+10a7b 27+10a-7b

Key Points to Remember

Essential concepts to master this topic
  • Negative Distribution: Distribute negative sign to every term inside parentheses
  • Sign Rules: Negative times negative equals positive: -(−2a) = +2a
  • Combine Like Terms: Group constants and same variables: 8a + 2a = 10a ✓

Common Mistakes

Avoid these frequent errors
  • Not distributing negative sign to all terms
    Don't just change the first term's sign and leave others unchanged = wrong simplification! This ignores proper distribution rules and gives incorrect coefficients. Always distribute the negative sign to every single term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

\( 100-(5+55)= \)

FAQ

Everything you need to know about this question

Why do I need to distribute the negative sign to every term?

+

The negative sign acts as -1 multiplied by everything in parentheses. Just like 2(3+4)=6+8 2(3+4) = 6+8 , we need (7b132a)=7b+13+2a -(7b-13-2a) = -7b+13+2a .

How do I know when to make a term positive or negative?

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Use the sign multiplication rules: negative times positive = negative, and negative times negative = positive. So (13)=+13 -(-13) = +13 and (2a)=+2a -(-2a) = +2a .

What's the difference between 8a and 2a when combining?

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Both have the same variable a, so they're like terms! Add their coefficients: 8a+2a=(8+2)a=10a 8a + 2a = (8+2)a = 10a . Think of it like 8 apples + 2 apples = 10 apples.

Why can't I combine 10a and 7b?

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They have different variables (a and b), making them unlike terms. You can only combine terms with the exact same variable and exponent.

How do I check if my final answer is correct?

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Substitute simple values for the variables back into both the original expression and your simplified answer. If they give the same result, you're correct! ✓

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