Simplify the Expression: 4a(a-b)+3b(a-b) Using Factoring

Q: How do I spot when I should factor instead of expand?

Look for identical expressions in parentheses! When you see the same binomial like (a-b) in multiple terms, that's your cue to factor it out first.

Q: What if the question asks me to simplify completely?

You can give either the factored form $ (4a + 3b)(a-b) $ or the expanded form $ 4a² - ab - 3b² $. Both are correct simplified forms!

Q: Why is factoring better than expanding here?

Factoring shows the structure of the expression more clearly. It's like organizing your room - everything has its proper place and relationships are easier to see.

Q: How do I distribute when factoring out the common term?

Think backwards! If $ (4a + 3b)(a-b) $ expands to our original expression, then $ 4a(a-b) + 3b(a-b) = (4a + 3b)(a-b) $.

Q: What if I make an algebra mistake when expanding to check?

Take it slow with distribution: $ (4a + 3b)(a-b) = 4a·a - 4a·b + 3b·a - 3b·b $. Then combine like terms: $ -4ab + 3ab = -ab $.

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

00:09 Positive times negative always equals negative

00:16 Open parentheses properly, multiply by each factor

00:22 Positive times negative always equals negative

00:31 Collect terms

00:38 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$4a(a-b)+3b(a-b)=$

2

Step-by-step solution

To solve this problem, we'll expand and simplify the given expression $4a(a-b) + 3b(a-b)$ by applying the distributive property.

Let's go through the steps:

Step 1: Apply the distributive property to the first term.
$4a(a-b) = 4a \cdot a - 4a \cdot b = 4a^2 - 4ab$
Step 2: Apply the distributive property to the second term.
$3b(a-b) = 3b \cdot a - 3b \cdot b = 3ab - 3b^2$
Step 3: Combine the results from Step 1 and Step 2.
Combine like terms: $4a^2 - 4ab + 3ab - 3b^2 = 4a^2 - ab - 3b^2$

Therefore, the simplified form of the expression is $4a^2 - ab - 3b^2$ .

Among the given choices, the correct answer is:

$4a^2-ab-3b^2$

3

Final Answer

$4a^2-ab-3b^2$

Key Points to Remember

Essential concepts to master this topic

Factor Recognition: Identify the common binomial factor (a-b) in both terms
Technique: Factor out (a-b): 4a(a-b) + 3b(a-b) = (4a + 3b)(a-b)
Check: Expand back: (4a + 3b)(a-b) = 4a² - 4ab + 3ab - 3b² = 4a² - ab - 3b² ✓

Common Mistakes

Avoid these frequent errors

Expanding instead of factoring first
Don't immediately distribute 4a(a-b) = 4a² - 4ab without noticing the pattern! This creates extra work and misses the elegant factored form. Always look for common factors like (a-b) appearing in multiple terms before expanding.

Practice Quiz

Test your knowledge with interactive questions

Are the expressions the same or not?

$$ 20x $$

$2\times10x$

FAQ

Everything you need to know about this question

How do I spot when I should factor instead of expand?

+

Look for identical expressions in parentheses! When you see the same binomial like (a-b) in multiple terms, that's your cue to factor it out first.

What if the question asks me to simplify completely?

+

You can give either the factored form $(4a + 3b)(a-b)$ or the expanded form $4a² - ab - 3b²$ . Both are correct simplified forms!

Why is factoring better than expanding here?

+

Factoring shows the structure of the expression more clearly. It's like organizing your room - everything has its proper place and relationships are easier to see.

How do I distribute when factoring out the common term?

+

Think backwards! If $(4a + 3b)(a-b)$ expands to our original expression, then $4a(a-b) + 3b(a-b) = (4a + 3b)(a-b)$ .

What if I make an algebra mistake when expanding to check?

+

Take it slow with distribution: $(4a + 3b)(a-b) = 4a·a - 4a·b + 3b·a - 3b·b$ . Then combine like terms: $-4ab + 3ab = -ab$ .

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Simplify the Expression: 4a(a-b)+3b(a-b) Using Factoring

Factoring Expressions with Common Binomial Terms

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Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I spot when I should factor instead of expand?

What if the question asks me to simplify completely?

Why is factoring better than expanding here?

How do I distribute when factoring out the common term?

What if I make an algebra mistake when expanding to check?

🌟 Unlock Your Math Potential

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