(4x-7)^2

Jasonbradley

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Jun 16, 2024

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Expanding (4x-7)^2

The expression (4x-7)^2 represents the square of the binomial (4x-7). To expand this expression, we can use the FOIL method or the square of a binomial pattern.

Expanding using FOIL

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

1. First: Multiply the first terms of each binomial: (4x) * (4x) = 16x^2
2. Outer: Multiply the outer terms of each binomial: (4x) * (-7) = -28x
3. Inner: Multiply the inner terms of each binomial: (-7) * (4x) = -28x
4. Last: Multiply the last terms of each binomial: (-7) * (-7) = 49

Now, add all the terms together: 16x^2 - 28x - 28x + 49

Finally, combine like terms: 16x^2 - 56x + 49

Expanding using the Square of a Binomial Pattern

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

In our case, a = 4x and b = 7. Applying the pattern:

(4x)^2 - 2(4x)(7) + (7)^2

Simplifying: 16x^2 - 56x + 49

Conclusion

Both methods lead to the same expanded form: 16x^2 - 56x + 49.

This expression represents a quadratic equation. It can be used in various applications, such as solving equations, graphing, and analyzing data.