Complete the Expression: (x+)(x-) = x²-121

Q: How do I recognize this is a difference of squares problem?

Look for the pattern $ x^2 - \text{number} $ on one side! The difference of squares formula $ (x+a)(x-a) = x^2 - a^2 $ creates this exact pattern.

Q: Do both blanks always have the same number?

Yes! In the difference of squares pattern $ (x+a)(x-a) $, both blanks must be the same value but with opposite signs.

Q: How can I check my answer quickly?

Use FOIL to expand your factored form: $ (x+11)(x-11) = x^2 - 11x + 11x - 121 = x^2 - 121 $. The middle terms should cancel out!

Q: Why does the middle term disappear when I expand?

That's the magic of difference of squares! When you have $ (x+a)(x-a) $, the middle terms $ +ax $ and $ -ax $ are opposites and cancel each other out.

Difference of Squares with Perfect Square Constants

Fill in the missing element to obtain a true expression:

$(x+_—)\cdot(x-_—)=x^2-121$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the missing value

00:06 We will use the shortened multiplication formulas

00:17 We'll substitute X as A

00:25 and 121 as B

00:29 We'll extract the root and find B

00:36 B is the missing term

00:41 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

Fill in the missing element to obtain a true expression:

$(x+_—)\cdot(x-_—)=x^2-121$

Step-by-step solution

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

Identify the given expression as a difference of squares.
Apply the formula for finding the missing term in $(x+a)(x-a) = x^2 - a^2$ .
Determine the values of $a$ to fill in the blanks.

Now, let's work through each step:
Step 1: The expression given is $(x+\_—)\cdot(x-\_—) = x^2-121$ . Recognize that $x^2 - 121$ is a difference of squares.
Step 2: We know from the difference of squares formula that $a^2 = 121$ .
Step 3: Solve for $a$ by taking the square root of both sides: $a = \sqrt{121} = 11$ .

This means the expression becomes: $(x+11)(x-11) = x^2 - 121$ .

Therefore, the missing element is $11$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Pattern: $(x+a)(x-a) = x^2 - a^2$ identifies difference of squares
Method: Find $a$ by taking square root: $\sqrt{121} = 11$
Verify: Expand $(x+11)(x-11) = x^2 - 121$ matches given expression ✓

Common Mistakes

Avoid these frequent errors

Forgetting to take the square root of the constant
Don't use 121 directly in the blanks = $(x+121)(x-121) = x^2 - 14641$ ! This gives the wrong constant term because you need the square root. Always take $\sqrt{121} = 11$ for the blanks.

Practice Quiz

Test your knowledge with interactive questions

Solve:

$$ (2+x)(2-x)=0 $$

FAQ

Everything you need to know about this question

How do I recognize this is a difference of squares problem?

Look for the pattern $x^2 - \text{number}$ on one side! The difference of squares formula $(x+a)(x-a) = x^2 - a^2$ creates this exact pattern.

What if the number isn't a perfect square?

If the constant term isn't a perfect square (like 120 or 130), then it cannot be factored using the difference of squares pattern with integers. Check your problem again!

Do both blanks always have the same number?

Yes! In the difference of squares pattern $(x+a)(x-a)$ , both blanks must be the same value but with opposite signs.

How can I check my answer quickly?

Use FOIL to expand your factored form: $(x+11)(x-11) = x^2 - 11x + 11x - 121 = x^2 - 121$ . The middle terms should cancel out!

Why does the middle term disappear when I expand?

That's the magic of difference of squares! When you have $(x+a)(x-a)$ , the middle terms $+ax$ and $-ax$ are opposites and cancel each other out.

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Complete the Expression: (x+)(x-) = x²-121

Difference of Squares with Perfect Square Constants

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I recognize this is a difference of squares problem?

What if the number isn't a perfect square?

Do both blanks always have the same number?

How can I check my answer quickly?

Why does the middle term disappear when I expand?

🌟 Unlock Your Math Potential

More Questions

Difference of squares

Fill the Blanks: Solve the Quadratic Equation (_+3)·(_-3) = x²-9

Solve the Quadratic Puzzle: Factoring x² - 64

Solve (x+3)(x-3)+(x+1)(x-1)=0: Perfect Square Differences

Verify the Equation: (x+5)(x+3) = x²-3²

Complete the Expression: (x+__)(x-__) = x²-121

Difference of Squares with Perfect Square Constants

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I recognize this is a difference of squares problem?

What if the number isn't a perfect square?

Do both blanks always have the same number?

How can I check my answer quickly?

Why does the middle term disappear when I expand?

🌟 Unlock Your Math Potential

More Questions

Difference of squares

Fill the Blanks: Solve the Quadratic Equation (_+3)·(_-3) = x²-9

Solve the Quadratic Puzzle: Factoring x² - 64

Solve (x+3)(x-3)+(x+1)(x-1)=0: Perfect Square Differences

Verify the Equation: (x+5)(x+3) = x²-3²

Complete the Expression: (x+)(x-) = x²-121