Simplify (3a-2)(2x+4): Distributive Property Practice

Q: Can I use distributive property when the variables are different like a and x?

Absolutely! The distributive property works with any variables or constants. Whether it's a, x, y, or numbers - the rule stays the same: multiply each term by each term.

Q: Why can't I combine 6ax and -4x in the final answer?

Because 6ax has both variables (a and x) while -4x only has x. You can only combine like terms - terms with exactly the same variables and exponents.

Q: Do I always get 4 terms when multiplying two binomials?

Yes, when you multiply (term + term)(term + term), you always get 4 products initially. Sometimes you can combine like terms afterward, but you always start with 4.

Q: What if I mess up the signs during distribution?

Take it one step at a time! First multiply $ 3a $ by both terms, then multiply $ -2 $ by both terms. Remember: negative times positive equals negative.

Q: How do I know my final expression is fully simplified?

Check if any terms have the same variables with same exponents. In $ 6ax + 12a - 4x - 8 $, all terms are different, so it's fully simplified!

Distributive Property with Different Variables

It is possible to use the distributive property to simplify the expression

$(3a-2)(2x+4)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:04 Open parentheses properly, multiply each factor by each factor

00:25 Let's calculate the multiplications

00:44 Positive times negative always equals negative

00:52 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

It is possible to use the distributive property to simplify the expression

$(3a-2)(2x+4)$

Step-by-step solution

To solve the problem, we will use the distributive property. Our goal is to expand and simplify the given expression by distributing each term separately:

Step 1: Multiply the first term of the first binomial, $3a$ , by each term in the second binomial $(2x+4)$ :
$3a \cdot 2x = 6ax$
$3a \cdot 4 = 12a$
Step 2: Multiply the second term of the first binomial, $-2$ , by each term in the second binomial $(2x+4)$ :
$-2 \cdot 2x = -4x$
$-2 \cdot 4 = -8$
Step 3: Combine all the products to write the expanded expression:
$6ax + 12a - 4x - 8$

Therefore, the simplified expression using the distributive property is $6ax + 12a - 4x - 8$ .

Thus, the correct answer is Yes, $6ax+12a-4x-8$ .

Final Answer

Yes, $6ax+12a-4x-8$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply each term in first binomial by every term in second
Technique: $3a \cdot 2x = 6ax$ and $-2 \cdot 4 = -8$
Check: Count terms: original has 2×2 structure, result should have 4 terms ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute the negative sign
Don't multiply -2 by only the first term of (2x+4) = incomplete distribution! This gives you missing terms and wrong coefficients. Always multiply each term in the first binomial by every single term in the second binomial.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Can I use distributive property when the variables are different like a and x?

Absolutely! The distributive property works with any variables or constants. Whether it's a, x, y, or numbers - the rule stays the same: multiply each term by each term.

Why can't I combine 6ax and -4x in the final answer?

Because 6ax has both variables (a and x) while -4x only has x. You can only combine like terms - terms with exactly the same variables and exponents.

Do I always get 4 terms when multiplying two binomials?

Yes, when you multiply (term + term)(term + term), you always get 4 products initially. Sometimes you can combine like terms afterward, but you always start with 4.

What if I mess up the signs during distribution?

Take it one step at a time! First multiply $3a$ by both terms, then multiply $-2$ by both terms. Remember: negative times positive equals negative.

How do I know my final expression is fully simplified?

Check if any terms have the same variables with same exponents. In $6ax + 12a - 4x - 8$ , all terms are different, so it's fully simplified!

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