%5E2.jpeg "(4x-7)^2")
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:
- First: Multiply the first terms of each binomial: (4x) * (4x) = 16x^2
- Outer: Multiply the outer terms of each binomial: (4x) * (-7) = -28x
- Inner: Multiply the inner terms of each binomial: (-7) * (4x) = -28x
- 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.