Simplify (3a-4)b+2: Applying the Distributive Property

Q: Why can't I combine 3ab and -4b at the end?

Different variables! The term 3ab has both a and b, while -4b has only b. You can only combine like terms with exactly the same variables and powers.

Q: How do I know when to stop simplifying?

Stop when you have no like terms left to combine. In $ 3ab-4b+2 $, each term has different variables or constants, so this is fully simplified!

Q: What if there was another b term like +5b?

Then you could combine! For example: $ 3ab-4b+5b+2 = 3ab+b+2 $. Only terms with the same variable parts can be added or subtracted.

Q: Does the distributive property always make expressions longer?

Not always! Sometimes distributing helps you combine like terms afterward. But in this case, we get three different types of terms that can't be combined further.

Q: Why is the answer 'No' when we did use the distributive property?

Good catch! The question asks if we can use it to simplify. We used it to expand, but the result $ 3ab-4b+2 $ isn't actually simpler than the original $ (3a-4)b+2 $!

Distributive Property with Non-Distributable Terms

Is it possible to use the distributive property to simplify the expression?

If so,what is its simplest form?

$(3a-4)b+2$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:03 Let's open brackets properly, multiply by each factor

00:18 Let's calculate the multiplications

00:23 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

Is it possible to use the distributive property to simplify the expression?

If so,what is its simplest form?

$(3a-4)b+2$

Step-by-step solution

We begin by opening the parentheses using the distributive property in order to simplify the expression:

$x(y+z)=xy+xz$ Note that in the distributive property formula we assume that there is addition between the terms inside of the parentheses, therefore it is crucial to take into account the sign of the coefficient of the term.

Furthermore, we apply the rules of multiplication of signs in order to present any expression within the parentheses. The parentheses are opened with the help of the distributive property, as an expression in which there is an addition operation between all the terms:

$(3a-4)b+2\\ \big(3a+(-4)\big)b+2$ We continue and open the parentheses using the distributive property:

$\big(3a+(-4)\big)b+2\\ 3a\cdot b+(-4)\cdot b +2\\ 3ab-4b+2$ Therefore, the correct answer is option c.

Final Answer

No, $3ab-4b+2$

Key Points to Remember

Essential concepts to master this topic

Rule: Only distribute when multiplication applies to entire parentheses
Technique: $(3a-4)b = 3ab-4b$ but +2 stays separate
Check: Verify no further combining possible: 3ab, -4b, +2 are all different ✓

Common Mistakes

Avoid these frequent errors

Trying to distribute the +2 to terms inside parentheses
Don't think +2 distributes to (3a-4) = 3a+2-4+2! The +2 is added after distribution, not multiplied. Always distribute only the factor directly connected to parentheses.

Practice Quiz

Test your knowledge with interactive questions

$(3+20)\times(12+4)=$

FAQ

Everything you need to know about this question

Why can't I combine 3ab and -4b at the end?

Different variables! The term 3ab has both a and b, while -4b has only b. You can only combine like terms with exactly the same variables and powers.

How do I know when to stop simplifying?

Stop when you have no like terms left to combine. In $3ab-4b+2$ , each term has different variables or constants, so this is fully simplified!

What if there was another b term like +5b?

Then you could combine! For example: $3ab-4b+5b+2 = 3ab+b+2$ . Only terms with the same variable parts can be added or subtracted.

Does the distributive property always make expressions longer?

Not always! Sometimes distributing helps you combine like terms afterward. But in this case, we get three different types of terms that can't be combined further.

Why is the answer 'No' when we did use the distributive property?

Good catch! The question asks if we can use it to simplify. We used it to expand, but the result $3ab-4b+2$ isn't actually simpler than the original $(3a-4)b+2$ !

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