Multiply (4y+3)(3x+2): Binomial Expression Expansion

Q: What does FOIL stand for and why is it important?

FOIL stands for First, Outer, Inner, Last. It helps you remember to multiply every combination of terms: First terms (4y × 3x), Outer terms (4y × 2), Inner terms (3 × 3x), and Last terms (3 × 2).

Q: Why can't I combine 12xy and 8y in the final answer?

These are not like terms! The term 12xy has both x and y variables, while 8y only has y. You can only combine terms that have exactly the same variables with the same powers.

Binomial Multiplication with Mixed Variables

Solve the following exercise:

$(4y+3)\cdot(3x+2)=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's solve this math problem together.

00:11 First, open the parentheses carefully. Multiply each number inside by every other number inside.

00:32 Next, calculate these multiplications step by step.

00:52 And that's how we find the solution to the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$(4y+3)\cdot(3x+2)=$

Step-by-step solution

To solve this problem, we'll expand and simplify the expression $(4y + 3)(3x + 2)$ by applying the distributive property. Let's go through the steps:

Step 1: Use the distributive property on $(4y + 3)(3x + 2)$ .
Step 2: Multiply each term in $(4y + 3)$ with each term in $(3x + 2)$ .
Step 3: Combine like terms if possible.

Now, let's perform these steps in detail:

Step 1: The expression is given as $(4y + 3)(3x + 2)$ . We'll expand this by multiplying each component:

$4y \cdot 3x = 12xy$
$4y \cdot 2 = 8y$
$3 \cdot 3x = 9x$
$3 \cdot 2 = 6$

Step 2: Combine all these products to form the expanded expression:

$12xy + 8y + 9x + 6$

Step 3: Verify if we can combine any like terms. In this case, all terms are different, so no combination is possible.

Thus, the simplified result of the expression $(4y+3)(3x+2)$ is: $12xy + 8y + 9x + 6$ .

This matches choice 1 from the provided options.

Final Answer

_{^{$12xy+8y+9x+6$}}

Key Points to Remember

Essential concepts to master this topic

FOIL Method: Multiply First, Outer, Inner, Last terms systematically
Technique: 4y × 3x = 12xy, then 4y × 2 = 8y
Check: Count terms: should have 4 terms before combining like terms ✓

Common Mistakes

Avoid these frequent errors

Only multiplying the first terms of each binomial
Don't just multiply 4y × 3x = 12xy and stop! This gives an incomplete answer missing three terms. The distributive property requires multiplying every term in the first binomial by every term in the second. Always use FOIL: First + Outer + Inner + Last.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

What does FOIL stand for and why is it important?

FOIL stands for First, Outer, Inner, Last. It helps you remember to multiply every combination of terms: First terms (4y × 3x), Outer terms (4y × 2), Inner terms (3 × 3x), and Last terms (3 × 2).

Why can't I combine 12xy and 8y in the final answer?

These are not like terms! The term 12xy has both x and y variables, while 8y only has y. You can only combine terms that have exactly the same variables with the same powers.

How do I keep track of all the multiplications?

Draw connecting lines! Connect each term in the first binomial to each term in the second binomial. This visual method ensures you don't miss any multiplications: 4 connections total.

What if the signs were different, like (4y + 3)(3x - 2)?

Follow the same FOIL process, but pay attention to signs! When you multiply 4y × (-2) = -8y and 3 × (-2) = -6. The final answer would be $12xy - 8y + 9x - 6$ .

Can I check my answer by plugging in numbers?

Yes! Try x = 1, y = 1. Original: (4×1+3)(3×1+2) = 7×5 = 35. Your answer: 12(1)(1) + 8(1) + 9(1) + 6 = 12 + 8 + 9 + 6 = 35 ✓

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Algebraic Technique questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime