%5E2-15.jpeg "(6x-7)^2-15")
Expanding and Simplifying the Expression (6x - 7)^2 - 15
This article explores the process of expanding and simplifying the algebraic expression (6x - 7)^2 - 15.
Understanding the Expression
The expression involves several operations:
- Squaring: The term (6x - 7)^2 represents the square of the binomial (6x - 7).
- Subtraction: The term - 15 is subtracted from the result of squaring the binomial.
Expanding the Square
To expand (6x - 7)^2, we can use the following formula:
(a - b)^2 = a^2 - 2ab + b^2
Applying this to our expression:
(6x - 7)^2 = (6x)^2 - 2(6x)(7) + (-7)^2
Simplifying:
(6x - 7)^2 = 36x^2 - 84x + 49
Combining Terms
Now, we combine the expanded square term with the constant term -15:
(6x - 7)^2 - 15 = (36x^2 - 84x + 49) - 15
Simplifying further:
(6x - 7)^2 - 15 = 36x^2 - 84x + 34
Final Simplified Expression
Therefore, the simplified form of the expression (6x - 7)^2 - 15 is 36x^2 - 84x + 34.
This expression represents a quadratic equation, with a leading coefficient of 36, a linear coefficient of -84, and a constant term of 34.