8m3+125n3 factorize
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Step-by-step explanation:
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 : 8 is the cube of 2
Check : 125 is the cube of 5
Check : m3 is the cube of m1
Check : n3 is the cube of n1
Factorization is :
(2m - 5n) • (4m2 + 10mn + 25n2)
Trying to factor a multi variable polynomial :
3.2 Factoring 4m2 + 10mn + 25n2
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Final result :
(2m - 5n) • (4m2 + 10mn + 25n2)
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