Expand the Expression: (2x+y)(x+3) Using Distribution Method

Q: Do I always get 4 terms when using FOIL?

Initially yes, but sometimes you can combine like terms to get fewer terms in your final answer. In this problem, no terms can be combined, so we keep all 4 terms.

Q: What if I forget one of the FOIL steps?

You'll get an incomplete answer! Use the box method as backup: draw a 2×2 grid and multiply each row header by each column header to make sure you get all 4 products.

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

Yes! The order doesn't matter for addition. You can write $ 2x^2 + xy + 6x + 3y $ or $ 2x^2 + 6x + xy + 3y $ - both are correct!

Binomial Multiplication with FOIL Method

$(2x+y)(x+3)=$

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Step-by-step video solution

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00:00 Solve

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

00:14 Calculate the multiplications

00:45 And this is the solution to the question

Step-by-step written solution

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Understand the problem

$(2x+y)(x+3)=$

Step-by-step solution

To solve this problem, we'll apply the FOIL method for multiplying binomials:

First: Multiply the first terms in each binomial: $(2x)(x) = 2x^2$ .
Outer: Multiply the outer terms in the product: $(2x)(3) = 6x$ .
Inner: Multiply the inner terms: $(y)(x) = xy$ .
Last: Multiply the last terms: $(y)(3) = 3y$ .

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

$2x^2 + 6x + xy + 3y$ .

Since terms $6x$ and $xy$ are not like terms, they cannot be combined, resulting in the final expression:

$2x^2 + xy + 6x + 3y$ .

Upon reviewing the multiple-choice options, the correct answer is the expanded expression, choice 4: $2x^2 + xy + 6x + 3y$ .

Final Answer

$2x^2+xy+6x+3y$

Key Points to Remember

Essential concepts to master this topic

FOIL Rule: First, Outer, Inner, Last terms must all be multiplied
Technique: $(2x)(x) = 2x^2$ and $(y)(3) = 3y$
Check: Count four terms in expansion: $2x^2 + xy + 6x + 3y$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying only some terms instead of all four combinations
Don't just multiply $(2x)(x) = 2x^2$ and $(y)(3) = 3y$ = incomplete answer like $2x^2 + 3y$ ! This misses the outer and inner products. Always multiply every term in the first binomial by every term in the second binomial using FOIL.

Practice Quiz

Test your knowledge with interactive questions

$$ (x+y)(x-y)= $$

FAQ

Everything you need to know about this question

What does FOIL stand for again?

First, Outer, Inner, Last! It's the order you multiply terms: first terms together, outer terms together, inner terms together, then last terms together.

Why can't I combine 6x and xy in the final answer?

Because 6x and xy are not like terms! Like terms must have exactly the same variables with the same exponents. Since one has just x and the other has xy, they stay separate.

Do I always get 4 terms when using FOIL?

Initially yes, but sometimes you can combine like terms to get fewer terms in your final answer. In this problem, no terms can be combined, so we keep all 4 terms.

What if I forget one of the FOIL steps?

You'll get an incomplete answer! Use the box method as backup: draw a 2×2 grid and multiply each row header by each column header to make sure you get all 4 products.

Can I rearrange the terms in my final answer?

Yes! The order doesn't matter for addition. You can write $2x^2 + xy + 6x + 3y$ or $2x^2 + 6x + xy + 3y$ - both are correct!

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