Question

Factorise 125m^3-64n^3​

Answer 1

Answer:

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STEP 1 :

Equation at the end of step 1

(125 • (m3)) - 26n3

STEP 2 :

Equation at the end of step 2

53m3 - 26n3

STEP 3 :

Trying to factor as a Difference of Cubes:

3.1 Factoring: 125m3-64n3

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 : 64 is the cube of 4

Check : m3 is the cube of m1

Check : n3 is the cube of n1

Factorization is :

(5m - 4n) • (25m2 + 20mn + 16n2)

Trying to factor a multi variable polynomial :

3.2 Factoring 25m2 + 20mn + 16n2

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

Factorization fails

Final result :

(5m - 4n) • (25m2 + 20mn + 16n2)

Hope it helps (^‿^)

Answer 2

Refer to the attached image ❤