Simplify (a+b)(c·g): Applying the Distributive Property

Q: Why can't I distribute to c and g separately?

Because $ c \cdot g $ is already multiplied together as one unit! It's like having the number 6 - you wouldn't break it into 2×3 when distributing. Treat $ (c \cdot g) $ as a single factor.

Q: How is this different from (a+b)(c+g)?

Great question! In $ (a+b)(c+g) $, you have addition inside both parentheses, so you distribute each term to each term. But $ (c \cdot g) $ is multiplication, making it one combined factor.

Q: What does 'acg + bcg' actually mean?

It means $ a \times c \times g $ plus $ b \times c \times g $. All three variables in each term are multiplied together. You can also factor this as $ cg(a + b) $ to check your work!

Q: Can I simplify acg + bcg further?

Yes! You can factor out the common factors $ cg $ to get $ cg(a + b) $, which takes you back to the original expression. This confirms your distribution was correct.

Q: Why does the question say 'No' for the correct answer?

The question asks if we can use distributive property to simplify the expression. Since $ acg + bcg $ is actually more complex than $ (a+b)(c \cdot g) $, we haven't truly simplified it - just expanded it!

Distributive Property with Product Factors

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

$(a+b)(c\cdot g)$

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Step-by-step video solution

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00:00 Simply

00:03 Open parentheses properly, multiply each factor by each factor

00:10 And this is the solution to the question

Step-by-step written solution

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Understand the problem

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

$(a+b)(c\cdot g)$

Step-by-step solution

To solve this problem, we must determine if we can apply the distributive property to simplify the expression $(a+b)(c \cdot g)$ .

The distributive property states that for any three terms, the expression $x(y+z)$ results in $xy + xz$ . Here, we have the sum $(a + b)$ and the product $(c \cdot g)$ .

We can treat $(c \cdot g)$ as a single term because it involves multiplication, which makes it like a single number or variable in terms of manipulating the expression algebraically. Therefore, using the distributive property, we distribute $(c \cdot g)$ over the terms within the parentheses:

Step 1: Distribute $c \cdot g$ to $a$ , yielding $acg$ .
Step 2: Distribute $c \cdot g$ to $b$ , yielding $bcg$ .

Hence, the simplified expression is:

$acg + bcg$ .

Therefore, the correct answer, according to the choices provided, is:

No, $acg + bcg$ .

Final Answer

No, $acg+\text{bcg}$

Key Points to Remember

Essential concepts to master this topic

Rule: Treat products like $c \cdot g$ as single terms when distributing
Technique: Distribute $(c \cdot g)$ to each term: $a(c \cdot g) + b(c \cdot g)$
Check: Final form $acg + bcg$ has same variables multiplied together ✓

Common Mistakes

Avoid these frequent errors

Distributing to individual variables instead of the entire product
Don't distribute $(a+b)$ to just $c$ and $g$ separately = $ac + ag + bc + bg$ ! This ignores that $c \cdot g$ is already multiplied together as one unit. Always treat products like $(c \cdot g)$ as single terms when applying distributive property.

Practice Quiz

Test your knowledge with interactive questions

Resolve -

$$ (x-3)(x-6)= $$

FAQ

Everything you need to know about this question

Why can't I distribute to c and g separately?

Because $c \cdot g$ is already multiplied together as one unit! It's like having the number 6 - you wouldn't break it into 2×3 when distributing. Treat $(c \cdot g)$ as a single factor.

How is this different from (a+b)(c+g)?

Great question! In $(a+b)(c+g)$ , you have addition inside both parentheses, so you distribute each term to each term. But $(c \cdot g)$ is multiplication, making it one combined factor.

What does 'acg + bcg' actually mean?

It means $a \times c \times g$ plus $b \times c \times g$ . All three variables in each term are multiplied together. You can also factor this as $cg(a + b)$ to check your work!

Can I simplify acg + bcg further?

Yes! You can factor out the common factors $cg$ to get $cg(a + b)$ , which takes you back to the original expression. This confirms your distribution was correct.

Why does the question say 'No' for the correct answer?

The question asks if we can use distributive property to simplify the expression. Since $acg + bcg$ is actually more complex than $(a+b)(c \cdot g)$ , we haven't truly simplified it - just expanded it!

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