%5E2-expand-and-simplify.jpeg "(x-3)^2 Expand And Simplify")
Expanding and Simplifying (x-3)^2
In algebra, understanding how to expand and simplify expressions is a fundamental skill. One common expression that often causes confusion is (x-3)^2. Let's break down how to expand and simplify this expression.
Understanding the Expression
The expression (x-3)^2 means that we are multiplying the binomial (x-3) by itself:
(x-3)^2 = (x-3)(x-3)
Using the FOIL Method
To expand the expression, we can use the FOIL method. FOIL stands for First, Outer, Inner, Last. This method helps us systematically multiply each term in the first binomial with each term in the second binomial.
- First: Multiply the first terms of each binomial: x * x = x^2
- Outer: Multiply the outer terms of the binomials: x * -3 = -3x
- Inner: Multiply the inner terms of the binomials: -3 * x = -3x
- Last: Multiply the last terms of the binomials: -3 * -3 = 9
Now we have: x^2 - 3x - 3x + 9
Simplifying the Expression
The final step is to combine like terms:
x^2 - 6x + 9
Therefore, the expanded and simplified form of (x-3)^2 is x^2 - 6x + 9.
Key Points
- (x-3)^2 is not the same as x^2 - 9. Remember to use the FOIL method to properly expand the expression.
- Simplifying involves combining like terms to obtain the most concise form.
By understanding the FOIL method and combining like terms, you can confidently expand and simplify expressions like (x-3)^2.