Simplify the Linear Expression: 4a+(5a-2)-4a+10

Q: Why do I need to eliminate parentheses first?

The order of operations requires you to handle parentheses before combining like terms. This ensures you distribute signs correctly and don't miss any terms!

Q: How do I know which terms are 'like terms'?

Like terms have the same variable with the same exponent. Here, 4a, 5a, and -4a are all like terms because they're all 'a to the first power'.

Q: What if I get confused with the signs?

Write each step clearly: $ 4a+(5a-2)-4a+10 = 4a+5a-2-4a+10 $. Then group: $ (4a+5a-4a)+(-2+10) $.

Q: Can I combine the numbers -2 and +10 right away?

Yes! Constant terms (numbers without variables) can be combined at any time: -2 + 10 = 8. Just make sure you handle the variable terms correctly first.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's solve this problem.

00:12 First, we'll rewrite it in a simpler form.

00:20 Using the commutative law, we arrange the terms to make it clearer.

00:52 Next, we follow the order of operations, working from left to right.

00:59 And that's how we find our solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$4a+(5a-2)-4a+10=$

2

Step-by-step solution

According to the rules of the order of operations, we first eliminate the parentheses.

Remember that a positive times a positive will give a positive result, and a positive times a negative will give a negative result.

Therefore, we obtain:

$4a+5a-2-4a+10=$

Now, we arrange the exercise in a more comfortable way using the substitution property:

$4a+5a-4a+10-2=$

We solve the exercise from left to right, starting by adding the coefficients a:

$4a+5a-4a=9a-4a=5a$

Now we obtain:

$5a+10-2=5a+8$

3

Final Answer

$5a+8$

Key Points to Remember

Essential concepts to master this topic

Distribution: Multiply signs through parentheses first to eliminate them
Collection: Group like terms: 4a + 5a - 4a = 5a
Check: Substitute a = 1: 4(1) + (5(1) - 2) - 4(1) + 10 = 13 ✓

Common Mistakes

Avoid these frequent errors

Ignoring the negative sign before parentheses
Don't forget that +(5a-2) means +5a-2 and -(5a-2) would mean -5a+2! Missing or mishandling signs changes your entire answer. Always carefully distribute the sign in front of parentheses to every term inside.

Practice Quiz

Test your knowledge with interactive questions

$$ 13+5+5= $$ ?

FAQ

Everything you need to know about this question

Why do I need to eliminate parentheses first?

+

The order of operations requires you to handle parentheses before combining like terms. This ensures you distribute signs correctly and don't miss any terms!

How do I know which terms are 'like terms'?

+

Like terms have the same variable with the same exponent. Here, 4a, 5a, and -4a are all like terms because they're all 'a to the first power'.

What if I get confused with the signs?

+

Write each step clearly: $4a+(5a-2)-4a+10 = 4a+5a-2-4a+10$ . Then group: $(4a+5a-4a)+(-2+10)$ .

Can I combine the numbers -2 and +10 right away?

+

Yes! Constant terms (numbers without variables) can be combined at any time: -2 + 10 = 8. Just make sure you handle the variable terms correctly first.

How do I check my final answer?

+

Pick any number for 'a' (like a = 2) and substitute it into both the original expression and your answer. If you get the same result, you're correct!

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Simplify the Linear Expression: 4a+(5a-2)-4a+10

Combining Like Terms with Parentheses

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