Example 3: Finding the square of a binomial with two variables | Algebra I | Khan Academy | Summary and Q&A

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November 24, 2010
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Example 3: Finding the square of a binomial with two variables | Algebra I | Khan Academy

TL;DR

You can find the area of a square with side length (6x-5y) by multiplying the width and height using the distributive property or by recognizing the pattern of squaring a binomial.

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Key Insights

  • ✖️ The area of a square can be found by multiplying the width and height.
  • ✖️ The distributive property can be used to simplify the multiplication of binomials.
  • 💨 Recognizing the pattern of squaring a binomial can provide a faster way to find the area.
  • ❎ The formula for the area of a square with side (6x-5y) is 36x^2 - 60xy + 25y^2.
  • ❓ Using the distributive property twice or applying the binomial squaring pattern both yield the same result.
  • 🥺 Understanding these concepts can lead to more efficient problem-solving in mathematical calculations.
  • ❓ It is important to recognize patterns and utilize them to simplify calculations.

Transcript

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Questions & Answers

Q: How can I find the area of a square with the side (6x-5y)?

To find the area of the square, multiply the width (6x-5y) by the height (6x-5y). This can be done using the distributive property or by recognizing the pattern of squaring a binomial.

Q: What is the formula for the area of the square?

The formula for the area of the square is (6x-5y) times (6x-5y), which simplifies to 36x^2 - 60xy + 25y^2.

Q: Is there a faster way to find the area of the square?

Yes, if you recognize the pattern of squaring a binomial, you can use the formula (a+b)^2 = a^2 + 2ab + b^2. In this case, (6x-5y)^2 simplifies to 36x^2 - 60xy + 25y^2.

Q: Can we use any other method to find the area of the square?

The distributive property or the binomial squaring pattern are the most efficient methods to find the area of the square. Other methods may be more time-consuming or prone to errors.

Summary & Key Takeaways

  • To find the area of a square with side length (6x-5y), multiply the width (6x-5y) by the height (6x-5y).

  • You can either use the distributive property or recognize the pattern of squaring a binomial to simplify the multiplication.

  • The simplified formula for the area of the square is 36x^2 - 60xy + 25y^2.

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