What's the Formula for the Square of a Difference?

Squaring means multiplying something by itself
Difference means subtraction
a and b are variables
Multiply out the left hand side to show that it equals the right hand side
Use the FOIL method to multiply (a-b)(a-b)
Simplify each term by multiplying
-ab-ab=-2ab
Since we got the right hand side when we multiplied out the left, our formula is correct

1. Squaring something means multiplying it times itself
2. A difference is a subtraction of two things
1. Squaring something means multiplying it times itself
2. A difference is a subtraction of two things
3. A binomial is a polynomial with two terms
1. a and b are variables
2. a-b is a difference, since we're subtracting
3. Squaring a-b means we are multiplying (a-b)(a-b)
1. We can check to make sure our formula is correct by multiplying out the left hand side
1. FOIL is a method we use to multiply two binomials together
1. a-b times a-b is the same as (a-b)²
1. FOIL is a method we use to multiply two binomials together
1. Multiply the first terms to get a•a
2. Multiply the outer terms to get a(-b)
3. Multiply the inner terms to get (-b)a
4. Multiply the last terms to get (-b)(-b)
1. Multiply the terms together to simplify
1. -ab and -ab have the same variables raised to the same power
2. So they are like terms and we can combine them
3. -ab-ab=-2ab
1. Since we got the right hand side of the formula when we multiplied the left, we know our formula is correct
1. Since we got the right hand side of the formula when we multiplied the left, we know our formula is correct

Definition: Square of a Difference