Solve the Expression: (xy+2a)(x-2b) Binomial Multiplication

Q: Why does xy times x equal x²y and not x²?

When multiplying xy × x, you multiply all parts: x × x = x² and y stays as y, giving you x²y. Think of it as (x)(y) × (x) = (x²)(y).

Q: How do I keep track of all the signs?

Write each multiplication step clearly: xy × (-2b) = -2xyb. The negative sign from -2b carries through to make the term negative.

Q: Can I rearrange the terms in my final answer?

Yes! $ x^2y - 2xyb + 2ax - 4ab $ could also be written as $ x^2y + 2ax - 2xyb - 4ab $. The order doesn't matter in addition.

Q: What if I get confused with so many variables?

Take it one step at a time! Write out each FOIL step separately before combining. It's better to be slow and accurate than fast and wrong.

Binomial Multiplication with Multivariable Terms

Solve the exercise:

$(xy+2a)\cdot(x-2b)=$

❤️ 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

00:00 Solve

00:04 Open parentheses properly, multiply each factor by each factor

00:26 Let's calculate the multiplications

00:54 Positive times negative always equals negative

01:03 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:

$(xy+2a)\cdot(x-2b)=$

Step-by-step solution

To solve the problem $(xy + 2a) \cdot (x - 2b)$ , we will use the distributive property, commonly referred to as the FOIL method for binomials. This involves multiplying each term in the first binomial by each term in the second binomial:

First: Multiply the first terms of each binomial: $xy \times x = x^2y$ .
Outside: Multiply the outer terms: $xy \times (-2b) = -2xyb$ .
Inside: Multiply the inner terms: $2a \times x = 2ax$ .
Last: Multiply the last terms: $2a \times (-2b) = -4ab$ .

Next, we combine these four results to form the expanded expression:

$x^2y - 2xyb + 2ax - 4ab$

Thus, the correct expression after using the distributive property and simplifying is $x^2y - 2xyb + 2ax - 4ab$ .

Final Answer

_{^{$x^2y-2xyb+2ax-4ab$}}

Key Points to Remember

Essential concepts to master this topic

FOIL Method: First, Outside, Inside, Last multiplication steps
Technique: xy × x = x²y, keep variables together
Check: Count terms: should have 4 terms after expanding ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply variables correctly
Don't just multiply coefficients and ignore variables = missing variable terms! When multiplying xy × x, the result is x²y, not just xy. Always multiply all parts of each term including variables and their exponents.

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

Why does xy times x equal x²y and not x²?

When multiplying xy × x, you multiply all parts: x × x = x² and y stays as y, giving you x²y. Think of it as (x)(y) × (x) = (x²)(y).

How do I keep track of all the signs?

Write each multiplication step clearly: xy × (-2b) = -2xyb. The negative sign from -2b carries through to make the term negative.

Can I rearrange the terms in my final answer?

Yes! $x^2y - 2xyb + 2ax - 4ab$ could also be written as $x^2y + 2ax - 2xyb - 4ab$ . The order doesn't matter in addition.

What if I get confused with so many variables?

Take it one step at a time! Write out each FOIL step separately before combining. It's better to be slow and accurate than fast and wrong.

How do I know I expanded correctly?

Count your terms! A binomial times a binomial should give you 4 terms before combining like terms. If you have fewer, you missed a multiplication.

🌟 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