a. x² - y² = (x + y)(x - y)
b. x⁶ - y⁶ = [(x - y)(x² + xy + y²)][(x + y)(x² - xy + y²)]
The problem has to do with simplification
What is simplification?
Simplification is the reduction of an expression into a simpler form
a. How to Simplify x² - y²
To simplify x² - y², we see that it is the difference of two squares.
So, x² - y² = (x + y)(x - y)
Thus, x² - y² = (x + y)(x - y)
b. How to simplify x⁶ - y⁶
To simplify x⁶ - y⁶, we re-wrire it in the form of difference of two squares.
So, x⁶ - y⁶ = (x³)² - (y³)²
= (x³ - y³)(x³ + y³)
Now (x³ - y³) is the difference of two cubes.
So, (x³ - y³) = (x - y)(x² + xy + y²)
Also, (x³ + y³) is the sum of two cubes.
So, (x³ + y³) = (x + y)(x² - xy + y²)
So, x⁶ - y⁶ = (x³)² - (y³)²
= (x³ - y³)(x³ + y³)
= [(x - y)(x² + xy + y²)][(x + y)(x² - xy + y²)]
So, x⁶ - y⁶ = [(x - y)(x² + xy + y²)][(x + y)(x² - xy + y²)]
Learn more about simplification here:
https://brainly.com/question/28060764
#SPJ1
