%5E2-expanded-form.jpeg "(3x-4)^2 Expanded Form")
Expanded Form of (3x-4)^2
In algebra, expanding a binomial expression like (3x-4)^2 means to multiply it by itself and combine like terms. In this article, we will explore the expanded form of (3x-4)^2 and learn how to derive it step by step.
The Formula
The formula for expanding a binomial expression (a-b)^2 is:
(a-b)^2 = a^2 - 2ab + b^2
Expanding (3x-4)^2
To expand (3x-4)^2, we can substitute a = 3x and b = 4 into the formula:
(3x-4)^2 = (3x)^2 - 2(3x)(4) + 4^2
Simplifying the Expression
Now, let's simplify the expression by calculating each term:
- (3x)^2 = 9x^2
- -2(3x)(4) = -24x
- 4^2 = 16
So, the expanded form of (3x-4)^2 is:
9x^2 - 24x + 16
Conclusion
In this article, we have successfully expanded (3x-4)^2 using the formula for expanding binomial expressions. The expanded form of (3x-4)^2 is 9x^2 - 24x + 16. This result can be used in various algebraic manipulations and problem-solving tasks.
