%5E2-simplify.jpeg "(3x-5)^2 Simplify")
Simplifying (3x - 5)^2
This article will guide you through simplifying the expression (3x - 5)^2.
Understanding the Expression
The expression (3x - 5)^2 represents the square of the binomial (3x - 5). This means we are multiplying the binomial by itself:
(3x - 5)^2 = (3x - 5)(3x - 5)
Using the FOIL Method
To simplify this expression, we can use the FOIL method:
- First: Multiply the first terms of each binomial: (3x)(3x) = 9x^2
- Outer: Multiply the outer terms of the binomials: (3x)(-5) = -15x
- Inner: Multiply the inner terms of the binomials: (-5)(3x) = -15x
- Last: Multiply the last terms of each binomial: (-5)(-5) = 25
Combining Like Terms
Now, we add all the terms together:
9x^2 - 15x - 15x + 25
Combining the like terms (-15x and -15x):
9x^2 - 30x + 25
Final Answer
Therefore, the simplified form of (3x - 5)^2 is 9x^2 - 30x + 25.
Important Note:
Remember that squaring a binomial is not the same as simply squaring each term individually. It's essential to use the FOIL method or other algebraic techniques to expand the expression correctly.