Expand (x+13)(y+4): Solving Two-Variable Binomial Products

Q: What does FOIL stand for and why do I need it?

FOIL stands for First, Outer, Inner, Last - the four ways to multiply terms in two binomials. It ensures you don't miss any combinations when expanding expressions like $ (x+13)(y+4) $.

Q: Can I just multiply the x terms and number terms separately?

No! That approach misses the cross terms. You must multiply every term in the first binomial by every term in the second binomial to get all four products.

Q: How do I remember which terms to multiply?

Use FOIL: First: x · y = xyOuter: x · 4 = 4xInner: 13 · y = 13yLast: 13 · 4 = 52

Q: Should I try to combine like terms in my final answer?

Only combine terms that have identical variable parts. In $ xy + 4x + 13y + 52 $, all terms are different, so this is already simplified!

Q: What if one binomial has subtraction instead?

FOIL still works! Just be careful with signs. For example, $ (x-3)(y+2) = xy + 2x - 3y - 6 $. Pay attention to positive and negative signs in each step.

Binomial Multiplication with Two Variables

$(x+13)(y+4)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve the problem.

00:10 First, open the parentheses. Remember to multiply each factor by every factor, step by step.

00:27 Now, carefully calculate each product. Take your time to ensure accuracy.

00:42 Great job! And that's the solution to our question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(x+13)(y+4)=$

Step-by-step solution

To solve this problem, we'll perform a step-by-step expansion of the expression $(x+13)(y+4)$ using the distributive property:

Step 1: Multiply the first terms $(x \cdot y) = xy$ .
Step 2: Multiply the outer terms $(x \cdot 4) = 4x$ .
Step 3: Multiply the inner terms $(13 \cdot y) = 13y$ .
Step 4: Multiply the last terms $(13 \cdot 4) = 52$ .

After completing these steps, combine the results:

$xy + 4x + 13y + 52$

This is the final expanded form of the expression. By comparing with the given choices, the correct answer is:

$xy + 4x + 13y + 52$

Therefore, the correct choice is option 3.

Final Answer

$xy+4x+13y+52$

Key Points to Remember

Essential concepts to master this topic

FOIL Method: First, Outer, Inner, Last terms multiply systematically
Technique: $(x+13)(y+4) = xy + 4x + 13y + 52$
Check: Count four terms in final answer: xy, 4x, 13y, 52 ✓

Common Mistakes

Avoid these frequent errors

Only multiplying first and last terms
Don't just multiply x·y = xy and 13·4 = 52 to get xy + 52! This skips the outer and inner terms, missing 4x + 13y completely. Always use FOIL to multiply all four combinations: 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 do I need it?

FOIL stands for First, Outer, Inner, Last - the four ways to multiply terms in two binomials. It ensures you don't miss any combinations when expanding expressions like $(x+13)(y+4)$ .

Can I just multiply the x terms and number terms separately?

No! That approach misses the cross terms. You must multiply every term in the first binomial by every term in the second binomial to get all four products.

How do I remember which terms to multiply?

Use FOIL:

First: x · y = xy
Outer: x · 4 = 4x
Inner: 13 · y = 13y
Last: 13 · 4 = 52

Should I try to combine like terms in my final answer?

Only combine terms that have identical variable parts. In $xy + 4x + 13y + 52$ , all terms are different, so this is already simplified!

What if one binomial has subtraction instead?

FOIL still works! Just be careful with signs. For example, $(x-3)(y+2) = xy + 2x - 3y - 6$ . Pay attention to positive and negative signs in each step.

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