Solve (x+y)(x-y): Expanding the Difference of Squares Formula

Q: Why does the middle term disappear when I use FOIL?

When you expand $(x+y)(x-y)$ with FOIL, you get $x^2 - xy + yx - y^2$. The terms $-xy$ and $+yx$ are additive inverses that cancel each other out!

Q: Can I just memorize the formula instead of using FOIL?

Yes! The difference of squares formula $(a+b)(a-b) = a^2 - b^2$ is faster once you recognize the pattern. Just identify what a and b are in your expression.

Q: What if the order is switched to (x-y)(x+y)?

The result is exactly the same! Multiplication is commutative, so $(x-y)(x+y) = (x+y)(x-y) = x^2 - y^2$. Order doesn't matter here.

Q: How is this different from (x+y)² or (x-y)²?

Those are perfect square formulas, not difference of squares! $(x+y)^2 = x^2 + 2xy + y^2$ and $(x-y)^2 = x^2 - 2xy + y^2$. Notice the middle terms don't cancel.

Q: Can I use this formula with numbers too?

Absolutely! For example: $(5+3)(5-3) = 8 \times 2 = 16$ or using the formula: $5^2 - 3^2 = 25 - 9 = 16$. Same answer!

Difference of Squares with Binomial Products

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

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Step-by-step video solution

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00:00 Solve

00:28 Open parentheses properly, multiply each factor by each factor

00:58 Collect terms

01:04 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

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

Step-by-step solution

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

Step 1: Identify the structure of the expression
Step 2: Apply the difference of squares formula
Step 3: Simplify the expression

Now, let's work through each step:
Step 1: The expression is $(x+y)(x-y)$ , which resembles the difference of squares. Step 2: Using the formula for the difference of squares, $(a+b)(a-b) = a^2 - b^2$ , we set $a = x$ and $b = y$ . Step 3: Applying the formula, we have:

$(x+y)(x-y) = x^2 - y^2$ .

Therefore, the solution to the problem is $x^2-y^2$ .

Final Answer

$x^2-y^2$

Key Points to Remember

Essential concepts to master this topic

Formula: $(a+b)(a-b) = a^2 - b^2$ for difference of squares
Technique: Identify $a = x$ and $b = y$ in $(x+y)(x-y)$
Check: Expand using FOIL: $x^2 - xy + yx - y^2 = x^2 - y^2$ ✓

Common Mistakes

Avoid these frequent errors

Using FOIL and forgetting to combine like terms
Don't expand to $x^2 - xy + yx - y^2$ and leave it there = wrong answer! The middle terms $-xy$ and $+yx$ are opposites and cancel out. Always combine like terms to get $x^2 - y^2$ .

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 the middle term disappear when I use FOIL?

When you expand $(x+y)(x-y)$ with FOIL, you get $x^2 - xy + yx - y^2$ . The terms $-xy$ and $+yx$ are additive inverses that cancel each other out!

Can I just memorize the formula instead of using FOIL?

Yes! The difference of squares formula $(a+b)(a-b) = a^2 - b^2$ is faster once you recognize the pattern. Just identify what a and b are in your expression.

What if the order is switched to (x-y)(x+y)?

The result is exactly the same! Multiplication is commutative, so $(x-y)(x+y) = (x+y)(x-y) = x^2 - y^2$ . Order doesn't matter here.

How is this different from (x+y)² or (x-y)²?

Those are perfect square formulas, not difference of squares! $(x+y)^2 = x^2 + 2xy + y^2$ and $(x-y)^2 = x^2 - 2xy + y^2$ . Notice the middle terms don't cancel.

Can I use this formula with numbers too?

Absolutely! For example: $(5+3)(5-3) = 8 \times 2 = 16$ or using the formula: $5^2 - 3^2 = 25 - 9 = 16$ . Same answer!

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