%5E2.jpeg "(x-4)^2")
The Square of a Binomial: (x-4)^2
In algebra, we often encounter expressions of the form (a+b)^2 or (a-b)^2, where a and b are constants or variables. In this article, we will explore the expansion of (x-4)^2, a specific case of the square of a binomial.
What is a Binomial?
A binomial is an algebraic expression consisting of two terms, usually written in the form a+b or a-b. In our case, we have x-4, where x is a variable and 4 is a constant.
Expanding (x-4)^2
To expand (x-4)^2, we need to follow the rule of squaring a binomial, which is:
(a+b)^2 = a^2 + 2ab + b^2
In our case, a = x and b = -4. Substituting these values into the formula, we get:
(x-4)^2 = x^2 - 2*4x + 4^2
= x^2 - 8x + 16
Simplifying the Expression
As we can see, the expanded form of (x-4)^2 is a quadratic expression, consisting of a squared term, a linear term, and a constant term. This expression can be used to solve various algebraic problems, such as finding the roots of a quadratic equation or graphing a parabola.
Conclusion
In conclusion, we have successfully expanded (x-4)^2 using the rule of squaring a binomial. The resulting expression, x^2 - 8x + 16, is a quadratic expression with a range of applications in algebra and mathematics.
