Solve (3a-4)(2+3a): Binomial Expression Multiplication

Q: What does FOIL stand for and why use it?

FOIL stands for First, Outer, Inner, Last - the four products you need when multiplying two binomials. It's a systematic way to make sure you don't miss any terms!

Q: Why do I get a higher degree term like 9a²?

When you multiply variable terms like $ 3a \cdot 3a $, you add the exponents: $ a^1 \cdot a^1 = a^2 $. This creates quadratic expressions from binomial multiplication.

Q: How do I know which terms are 'like terms' to combine?

Like terms have the same variable part. In this problem, $ 6a $ and $ -12a $ are like terms because both have just 'a', so combine them: $ 6a - 12a = -6a $.

Q: What's the correct order for writing my final answer?

Write polynomial terms in descending order of exponents: highest degree first. So $ 9a^2 - 6a - 8 $ is correct (degree 2, then degree 1, then constant).

Q: Can I check my answer by substituting a value for a?

Yes! Pick any value like $ a = 1 $. Original: $ (3-4)(2+3) = (-1)(5) = -5 $. Your answer: $ 9 - 6 - 8 = -5 $ ✓

Binomial Multiplication with FOIL Method

Solve the exercise:

$(3a-4)\cdot(2+3a)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

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

00:25 Calculate the products

00:47 Positive times negative always equals negative

00:57 Arrange the expression, group factors

01:06 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

Solve the exercise:

$(3a-4)\cdot(2+3a)=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Apply the distributive property using the FOIL method.
Step 2: Simplify the expression.
Step 3: Identify the final simplified polynomial expression.

Now, let’s work through each step:

Step 1: Apply the FOIL method:
(First) Multiply the first terms of each binomial: $3a \cdot 2 = 6a$ .
(Outer) Multiply the outer terms: $3a \cdot 3a = 9a^2$ .
(Inner) Multiply the inner terms: $-4 \cdot 2 = -8$ .
(Last) Multiply the last terms of each binomial: $-4 \cdot 3a = -12a$ .

Step 2: Combine the results:
Starting with each term from FOIL: $6a + 9a^2 - 8 - 12a$ .
Simplify by combining like terms: $9a^2 + (6a - 12a) - 8 = 9a^2 - 6a - 8$ .

Step 3: Identify the resulting polynomial expression:
The expression simplifies to $9a^2 - 6a - 8$ .

Therefore, the solution to the problem is $9a^2 - 6a - 8$ .

Final Answer

$9a^2-6a-8$

Key Points to Remember

Essential concepts to master this topic

FOIL Rule: Multiply First, Outer, Inner, Last terms systematically
Technique: $3a \cdot 2 = 6a$ , then $3a \cdot 3a = 9a^2$
Check: Combine like terms: $6a - 12a = -6a$ gives final answer ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply all four term combinations
Don't just multiply $3a \cdot 2 = 6a$ and stop = incomplete expansion! This misses three other products and gives wrong answers like $6a$ . Always use FOIL to multiply all four combinations: First, Outer, Inner, Last terms.

Practice Quiz

Test your knowledge with interactive questions

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

What is its simplified form?

$$ (ab)(c d) $$

$$

FAQ

Everything you need to know about this question

What does FOIL stand for and why use it?

FOIL stands for First, Outer, Inner, Last - the four products you need when multiplying two binomials. It's a systematic way to make sure you don't miss any terms!

Why do I get a higher degree term like 9a²?

When you multiply variable terms like $3a \cdot 3a$ , you add the exponents: $a^1 \cdot a^1 = a^2$ . This creates quadratic expressions from binomial multiplication.

How do I know which terms are 'like terms' to combine?

Like terms have the same variable part. In this problem, $6a$ and $-12a$ are like terms because both have just 'a', so combine them: $6a - 12a = -6a$ .

What's the correct order for writing my final answer?

Write polynomial terms in descending order of exponents: highest degree first. So $9a^2 - 6a - 8$ is correct (degree 2, then degree 1, then constant).

Can I check my answer by substituting a value for a?

Yes! Pick any value like $a = 1$ . Original: $(3-4)(2+3) = (-1)(5) = -5$ . Your answer: $9 - 6 - 8 = -5$ ✓

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