%5E2.jpeg "(2x/7-7y/4)^2")
Expanding the Square of a Binomial: (2x/7 - 7y/4)^2
This article will focus on expanding the expression (2x/7 - 7y/4) squared. We'll use the fundamental principles of squaring a binomial, and demonstrate the step-by-step process.
Understanding the Basics
The square of a binomial is simply the binomial multiplied by itself. In our case:
**(2x/7 - 7y/4)**² = (2x/7 - 7y/4) * (2x/7 - 7y/4)
Applying the FOIL Method
To expand the product, we can use the FOIL method, which stands for First, Outer, Inner, Last. This method helps us systematically multiply all terms in the binomials.
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First: Multiply the first terms of each binomial: (2x/7) * (2x/7) = 4x²/49
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Outer: Multiply the outer terms of the binomials: (2x/7) * (-7y/4) = -xy
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Inner: Multiply the inner terms of the binomials: (-7y/4) * (2x/7) = -xy
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Last: Multiply the last terms of each binomial: (-7y/4) * (-7y/4) = 49y²/16
Combining Like Terms
After applying the FOIL method, we get:
4x²/49 - xy - xy + 49y²/16
Combining the like terms (-xy and -xy), we obtain the final expanded form:
4x²/49 - 2xy + 49y²/16
Conclusion
Therefore, the expanded form of (2x/7 - 7y/4) squared is 4x²/49 - 2xy + 49y²/16. By understanding the FOIL method and applying it systematically, you can effectively expand any binomial squared expression.