hey guys, neeed help factorising these completely.
1. y^7 - y^3
2. y^5 * x^3 + y^3 * x^5
thank u!!!
$\displaystyle y^7 - y^3$
First, start by taking out the largest common factor between the two terms:
$\displaystyle y^3 \cdot y^4 - y^3 \cdot 1$
$\displaystyle y^3(y^4 - 1)$
Now, note that the expression in parenthesis is the difference between two perfect squares:
$\displaystyle y^4 - 1 = (y^2)^2 - 1^2 = (y^2 + 1)(y^2 - 1)$
So we have
$\displaystyle y^7 - y^3 = y^3(y^2 + 1)(y^2 - 1)$
Note that the last factor is also the difference of two squares, so we finally have:
$\displaystyle y^7 - y^3 = y^3(y^2 + 1)(y + 1)(y - 1)$
See what you can do with the second one. It starts off pretty much the same way as this one.
-Dan
hey for the 2nd question, i got this using your tactic.. thanks for that.. can you please check if ive done it correctly for the 2nd one.
$\displaystyle
y^5 \cdot x^3 + y^3 \cdot x^5
$
$\displaystyle
y^2 \cdot x^2 (y^3+x^3)
$
$\displaystyle
y^2 \cdot x^2 (x+y)(x^2-x \cdot y+y^2)
$
P.S i tryed to take out the y^3 and x^3 first but that would leave me with (y^2 + x^2) and i dont think that can be factorized??