# Math Help - Factorising...

1. ## Factorising...

hey guys, neeed help factorising these completely.

1. y^7 - y^3

2. y^5 * x^3 + y^3 * x^5

thank u!!!

2. Originally Posted by jvignacio
1. y^7 - y^3

2. y^5 * x^3 + y^3 * x^5
$y^7 - y^3$

First, start by taking out the largest common factor between the two terms:
$y^3 \cdot y^4 - y^3 \cdot 1$

$y^3(y^4 - 1)$

Now, note that the expression in parenthesis is the difference between two perfect squares:
$y^4 - 1 = (y^2)^2 - 1^2 = (y^2 + 1)(y^2 - 1)$

So we have
$y^7 - y^3 = y^3(y^2 + 1)(y^2 - 1)$

Note that the last factor is also the difference of two squares, so we finally have:
$y^7 - y^3 = y^3(y^2 + 1)(y + 1)(y - 1)$

See what you can do with the second one. It starts off pretty much the same way as this one.

-Dan

3. 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.

$
y^5 \cdot x^3 + y^3 \cdot x^5
$

$
y^2 \cdot x^2 (y^3+x^3)
$

$
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??