Question

64m+n factorise the following ​

Answer 1

hi64m3+125n3

Final result :

(4m + 5n) • (16m2 - 20mn + 25n2)

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(64 • (m3)) + 53n3

Step 2 :

Equation at the end of step 2 :

26m3 + 53n3

Step 3 :

Trying to factor as a Sum of Cubes :

3.1 Factoring: 64m3+125n3

Theory : A sum 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 : 64 is the cube of 4

Check : 125 is the cube of 5

Check : m3 is the cube of m1

Check : n3 is the cube of n1

Factorization is :

(4m + 5n) • (16m2 - 20mn + 25n2)

Trying to factor a multi variable polynomial :

3.2 Factoring 16m2 - 20mn + 25n2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result :

(4m + 5n) • (16m2 - 20mn + 25n2)

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