Simplify the Expression: 8y+45-34y-45z Step-by-Step

Q: Why can't I add 8y and 45z together?

Because y and z represent different unknown values! It's like trying to add 8 apples + 45 zebras - they're completely different things. You can only combine terms with identical variables.

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

Like terms have exactly the same variable with the same exponent. In $ 8y+45-34y-45z $, only 8y and -34y are like terms because they both have variable y.

Q: Can I rearrange the terms in any order?

Yes! You can rearrange terms freely as long as you keep the correct signs. Just remember that -34y means the coefficient is negative 34, not positive.

Q: Is -26y + 45 - 45z the same as 45 - 26y - 45z?

Absolutely! Both expressions are equivalent because addition and subtraction are commutative. You can write the terms in any order as long as the signs stay with the right terms.

Combining Like Terms with Multiple Variables

Simplify the following expression:

$8y+45-34y-45z=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify the expression

00:04 Mark the appropriate unknowns

00:09 Use the commutative law and arrange equal unknowns together

00:20 Group like terms

00:32 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

Simplify the following expression:

$8y+45-34y-45z=\text{?}$

Step-by-step solution

In order to solve this question, remember that we can perform the addition and subtraction operations when we have the same variable.
However we are limited when we have several different variables.

Note that in this exercise that we have three variables:
$45$ which has no variable
$8y$ and $34y$ which both have the variable $y$
and $45z$ with the variable $z$

Therefore, we can only operate with the y variable, since it's the only one that exists in more than one term.

Rearrange the exercise:

$45-34y+8y-45z$

Combine the relevant terms with $y$

$45-26y-45z$

We observe that this is similar to one of the other answers, with a small rearrangement of the terms:

$-26y+45-45z$

Given that we have no possibility to perform additional operations - this is the solution!

Final Answer

^{$-26y+45-45z$}

Key Points to Remember

Essential concepts to master this topic

Rule: Only combine terms with the same variable and exponent
Technique: Group like terms: 8y - 34y = -26y
Check: Count variable types: y terms, z terms, and constants ✓

Common Mistakes

Avoid these frequent errors

Combining terms with different variables
Don't combine 8y with 45z or 45 = wrong simplification! Variables y and z are completely different, like adding apples to oranges. Always only combine terms that have identical variables.

Practice Quiz

Test your knowledge with interactive questions

Are the expressions the same or not?

$$ 3+3+3+3 $$

$3\times4$

FAQ

Everything you need to know about this question

Why can't I add 8y and 45z together?

Because y and z represent different unknown values! It's like trying to add 8 apples + 45 zebras - they're completely different things. You can only combine terms with identical variables.

What do I do with the constant 45 that has no variable?

Constants (numbers without variables) are their own group! In this expression, 45 stands alone because there are no other constant terms to combine it with.

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

Like terms have exactly the same variable with the same exponent. In $8y+45-34y-45z$ , only 8y and -34y are like terms because they both have variable y.

Can I rearrange the terms in any order?

Yes! You can rearrange terms freely as long as you keep the correct signs. Just remember that -34y means the coefficient is negative 34, not positive.

Is -26y + 45 - 45z the same as 45 - 26y - 45z?

Absolutely! Both expressions are equivalent because addition and subtraction are commutative. You can write the terms in any order as long as the signs stay with the right terms.

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