(2y-7)^2

Jasonbradley

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Jun 16, 2024

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Expanding (2y - 7)^2

The expression (2y - 7)^2 represents the square of the binomial (2y - 7). To expand this expression, we can use the FOIL method or the square of a binomial formula.

Expanding using FOIL

FOIL stands for First, Outer, Inner, Last. This method helps us to multiply two binomials:

1. First: Multiply the first terms of each binomial: 2y * 2y = 4y^2
2. Outer: Multiply the outer terms of each binomial: 2y * -7 = -14y
3. Inner: Multiply the inner terms of each binomial: -7 * 2y = -14y
4. Last: Multiply the last terms of each binomial: -7 * -7 = 49

Now, combine the terms:

4y^2 - 14y - 14y + 49 = 4y^2 - 28y + 49

Expanding using the Square of a Binomial Formula

The square of a binomial formula states: (a - b)^2 = a^2 - 2ab + b^2

Applying this formula to our expression:

(2y - 7)^2 = (2y)^2 - 2(2y)(7) + (7)^2

Simplifying the terms:

(2y)^2 - 2(2y)(7) + (7)^2 = 4y^2 - 28y + 49

Conclusion

Both methods lead to the same expanded form: 4y^2 - 28y + 49. Remember that understanding these methods is crucial for simplifying and manipulating algebraic expressions.