Factorise 125x3+ y3 help me
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Answer:
2.1 Factoring: 125x3-y3
Theory : A difference of two perfect cubes, a3 - b3 can be factored into
(a-b) • (a2 +ab +b2)
Proof : (a-b)•(a2+ab+b2) =
a3+a2b+ab2-ba2-b2a-b3 =
a3+(a2b-ba2)+(ab2-b2a)-b3 =
a3+0+0-b3 =
a3-b3
Check : 125 is the cube of 5
Check : x3 is the cube of x1
Check : y3 is the cube of y1
Factorization is :
(5x - y) • (25x2 + 5xy + y2)
Trying to factor a multi variable polynomial :
2.2 Factoring 25x2 + 5xy + y2
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Final result :
(5x - y) • (25x2 + 5xy + y2)
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