%5E2-expand.jpeg "(y-1)^2 Expand")
Expanding (y-1)^2
The expression (y-1)^2 represents the square of the binomial (y-1). To expand it, we can use the following methods:
Method 1: Using the FOIL method
FOIL stands for First, Outer, Inner, Last. This method helps us multiply two binomials by systematically multiplying each term of the first binomial with each term of the second binomial.
- First: Multiply the first terms of each binomial: y * y = y^2
- Outer: Multiply the outer terms of the binomials: y * -1 = -y
- Inner: Multiply the inner terms of the binomials: -1 * y = -y
- Last: Multiply the last terms of each binomial: -1 * -1 = 1
Now, add all the terms together: y^2 - y - y + 1 = y^2 - 2y + 1
Method 2: Using the pattern (a-b)^2 = a^2 - 2ab + b^2
This formula directly applies to our expression, where a = y and b = 1.
Substituting the values: y^2 - 2(y)(1) + 1^2 = y^2 - 2y + 1
Conclusion
Both methods lead to the same expanded form of (y-1)^2, which is y^2 - 2y + 1. It's important to remember these methods and practice applying them to various binomial expressions.