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(3x-7y)^2

2 min read Jun 16, 2024
(3x-7y)^2

Squaring a Binomial: (3x - 7y)²

In algebra, squaring a binomial is a common operation that involves multiplying a binomial by itself. This article will explore how to expand the expression (3x - 7y)².

Understanding the Concept

The expression (3x - 7y)² represents the product of (3x - 7y) multiplied by itself:

(3x - 7y)² = (3x - 7y) * (3x - 7y)

Expanding the Expression

To expand this expression, we can use the FOIL method, which stands for First, Outer, Inner, Last.

  • First: Multiply the first terms of each binomial: (3x) * (3x) = 9x²
  • Outer: Multiply the outer terms of each binomial: (3x) * (-7y) = -21xy
  • Inner: Multiply the inner terms of each binomial: (-7y) * (3x) = -21xy
  • Last: Multiply the last terms of each binomial: (-7y) * (-7y) = 49y²

Now, combine the results:

9x² - 21xy - 21xy + 49y²

Finally, simplify by combining like terms:

9x² - 42xy + 49y²

Conclusion

Therefore, the expanded form of (3x - 7y)² is 9x² - 42xy + 49y². This process demonstrates how to square a binomial by applying the FOIL method and simplifying the resulting expression.

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