Factorise (25-10y)^3 + y^2 (25-10y)^2

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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Factorize:

`(25 -10y)^3 + y^2 (25-10y)^2`

The common factor here (present on both the left and right hand sides of the negative (-) symbol is: `(25 - 10y)^2` .

`therefore =(25 - 10y)^2 [ (25-10y) +y^2 (1)]`

Now consolidate the bracket :

`therefore = (25-10y)^2( 25 - 10y +y^2)`

Now factorize the second bracket. Note that we need the factors of the first (`25 times 1 or 5 times 5)`  and the factors of the third(`y times y)` which when combined  must render the middle term. Thus

`5 times y and 5 times y ` give us `10y` which we need to be negative thus

`5 times - y and 5 times -y` when added together  equal -10y 

`therefore = (25 -10y)^2 ( 5-y)^2`  

 

 

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