Simplify the Expression: -2+4a+4-2a+3-2a

Q: Why do the variable terms disappear completely?

The a-terms have coefficients that add to zero: $ 4a - 2a - 2a = 0a = 0 $. When a variable's coefficient becomes zero, that entire term disappears from the expression!

Q: Can I rearrange the terms in any order?

Yes! Addition and subtraction allow you to use the commutative property. Grouping like terms together makes the problem much easier to solve.

Q: What if I get confused by all the negative signs?

Write each term with its sign: $ (-2) + (+4a) + (+4) + (-2a) + (+3) + (-2a) $. This makes it clearer which terms are being added or subtracted.

Q: How do I know when I'm done simplifying?

You're done when you have no more like terms to combine. In this case, all variable terms canceled out, leaving only the constant $ 5 $.

Q: What does 'like terms' actually mean?

Like terms: Same variable with same exponent (4a, -2a, -2a)Constants: Numbers without variables (-2, 4, 3)Only like terms can be combined together!

Combining Like Terms with Signed Numbers

$-2+4a+4-2a+3-2a=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We'll use the commutative law and arrange the exercise to make it easier to solve

00:13 We'll group terms according to the associative law

00:35 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

$-2+4a+4-2a+3-2a=$

Step-by-step solution

We can use the substitutive property and arrange the exercise in a way that makes solving the exercise simpler:

$-2+4+3+4a-2a-2a=$

First, we solve the addition exercise:

$4+3=7$

We now obtain the exercise:

$-2+7+4a-2a-2a=$

We add the coefficients a:

$4a-2a=2a$

$2a-2a=0$

We now obtain the exercise:

$-2+7+0=$

We use the substitutive property:

$7-2+0=5+0=5$

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

Order: Group constants separately from variable terms first
Technique: Add coefficients: 4a - 2a - 2a = 0a = 0
Check: Substitute any value for a: -2 + 4(1) + 4 - 2(1) + 3 - 2(1) = 5 ✓

Common Mistakes

Avoid these frequent errors

Adding variable terms to constant terms incorrectly
Don't combine 4a with 4 to get 8a = wrong variable coefficient! Variable terms and constants are completely different and cannot be combined. Always keep constants separate from variable terms when simplifying.

Practice Quiz

Test your knowledge with interactive questions

$$ 94+12+6= $$

FAQ

Everything you need to know about this question

Why do the variable terms disappear completely?

The a-terms have coefficients that add to zero: $4a - 2a - 2a = 0a = 0$ . When a variable's coefficient becomes zero, that entire term disappears from the expression!

Can I rearrange the terms in any order?

Yes! Addition and subtraction allow you to use the commutative property. Grouping like terms together makes the problem much easier to solve.

What if I get confused by all the negative signs?

Write each term with its sign: $(-2) + (+4a) + (+4) + (-2a) + (+3) + (-2a)$ . This makes it clearer which terms are being added or subtracted.

How do I know when I'm done simplifying?

You're done when you have no more like terms to combine. In this case, all variable terms canceled out, leaving only the constant $5$ .

What does 'like terms' actually mean?

Like terms: Same variable with same exponent (4a, -2a, -2a)
Constants: Numbers without variables (-2, 4, 3)
Only like terms can be combined together!

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