%5E2-expanded.jpeg "(3x-3)^2 Expanded")
Expanding the Expression (3x-3)^2
In algebra, expanding an expression means to multiply out the brackets and simplify the resulting equation. In this article, we will explore how to expand the expression (3x-3)^2.
The Formula for Expanding (a+b)^2
Before we dive into expanding (3x-3)^2, let's recall the formula for expanding (a+b)^2:
(a+b)^2 = a^2 + 2ab + b^2
This formula can be applied to any expression of the form (a+b)^2, where a and b are constants, variables, or combinations of both.
Expanding (3x-3)^2
To expand (3x-3)^2, we can apply the formula above by substituting a = 3x and b = -3. This gives us:
(3x-3)^2 = (3x)^2 + 2(3x)(-3) + (-3)^2
Simplifying the Expression
Now, let's simplify each term in the expression:
(3x)^2 = 9x^2(since(3x)(3x) = 9x^2)2(3x)(-3) = -18x(since2(3x)(-3) = 2(3)(-3)x = -18x)(-3)^2 = 9(since(-3)(-3) = 9)
Substituting these values back into the expression, we get:
(3x-3)^2 = 9x^2 - 18x + 9
And there you have it! The expanded form of (3x-3)^2 is 9x^2 - 18x + 9.
Conclusion
In this article, we have successfully expanded the expression (3x-3)^2 using the formula (a+b)^2 = a^2 + 2ab + b^2. By substituting a = 3x and b = -3, we were able to simplify the expression to 9x^2 - 18x + 9.
