Simplify a(b+c): Using the Distributive Property in Algebra

Q: Why can't I just ignore the parentheses and write abc?

Because parentheses show addition, not multiplication! $ a(b+c) $ means "a times the sum of b and c", which is different from "a times b times c".

Q: What if there are more than two terms in parentheses?

The same rule applies! For $ a(b+c+d) $, you get $ ab + ac + ad $. Every term inside gets multiplied by the outside term.

Q: Can I use the distributive property backwards?

Yes! This is called factoring. If you see $ ab + ac $, you can factor out the common $ a $ to get $ a(b+c) $.

Q: What if the term outside is negative?

The distributive property still works! For $ -a(b+c) $, you get $ -ab - ac $. Remember: negative times positive equals negative.

Q: How do I know if I applied it correctly?

Try factoring your answer back to the original form. If $ ab + ac $ factors back to $ a(b+c) $, you did it right!

Distributive Property with Algebraic Terms

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

$a(b+c)$

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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 by each factor

00:10 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

$a(b+c)$

Step-by-step solution

To solve the problem and apply the distributive property correctly, follow these steps:

Identify the expression, which is $a(b+c)$ .
Apply the distributive property: multiply $a$ by each term inside the parentheses.

Applying this, we get:

$a \times b = ab$
$a \times c = ac$

Combine these two products:

The simplified expression is: $ab + ac$ .

This matches with answer choice 2: Yes, the answer $ab+ac$ .

Final Answer

Yes, the answer $ab+ac$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply the outside term by each term inside parentheses
Technique: For $a(b+c)$ , multiply: $a \times b = ab$ and $a \times c = ac$
Check: Factor your answer back: $ab + ac = a(b+c)$ matches original ✓

Common Mistakes

Avoid these frequent errors

Only multiplying the first term inside parentheses
Don't multiply just $a \times b = ab$ and forget about $c$ = wrong answer $ab + c$ ! This violates the distributive property because every term inside parentheses must be multiplied. Always multiply the outside term by each and every term inside the 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 just ignore the parentheses and write abc?

Because parentheses show addition, not multiplication! $a(b+c)$ means "a times the sum of b and c", which is different from "a times b times c".

What if there are more than two terms in parentheses?

The same rule applies! For $a(b+c+d)$ , you get $ab + ac + ad$ . Every term inside gets multiplied by the outside term.

Can I use the distributive property backwards?

Yes! This is called factoring. If you see $ab + ac$ , you can factor out the common $a$ to get $a(b+c)$ .

What if the term outside is negative?

The distributive property still works! For $-a(b+c)$ , you get $-ab - ac$ . Remember: negative times positive equals negative.

How do I know if I applied it correctly?

Try factoring your answer back to the original form. If $ab + ac$ factors back to $a(b+c)$ , you did it right!

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