A Difference Of Squares Math

A 2 b 2.

A difference of squares math. This method only works for difference of two squares and not for the sum of two squares. For example x 25 can be factored as x 5 x 5. Factoring the difference of the two squares gives. X 5 x 5 x 5 x 5.

A 2 b 2 a b a b this is because a b a b a 2 ab ab b 2 a 2 b 2. The factors of 25 are 5 and 5 besides 1 and itself. X 2 25 0 x 2 5 2 0 x 5 x 5 0 we get two values for x. A 2 b 2 a b a b this is true because a b a b a 2 ab ab b 2 a 2 b 2.

X 2 25 is not factorable since you re adding 25 not subtracting. A positive multiplied by a negative is always a negative. The first is the difference of squares formula. A b then we can factor it as a b a b.

So a difference of squares is something that looks like x 2 4. Where both the first and last term are perfect squares. Remember from your translation skills that a difference means a subtraction. A2 b2 a b a b.

When we factor a difference of two squares we will get. The difference of squares. When an expression can be viewed as the difference of two perfect squares i e. Let s conceptualize the difference of squares through investigation by removing square arrays from larger square arrays and rearranging to determine the new result.

A3 b3 a b a2 ab b2 using a geometric representation of difference of cubes similar to the approach used to derive the difference of squares formula in the video prove the difference of cubes formula to be true. I can remember first learning as a high school student and then teaching as a high school teacher the difference of squares property right in the middle of a quadratics factoring. Similar to difference of squares there is an identity formula for a difference of cubes. If you were to factor it you would have to use imaginary numbers such as i5.

That s because 4 2 2 so we really have x 2 2 2 which is a difference of squares.