Question

factorise: 27 m3 +64n3

Answer 1

Step-by-step explanation:

Step by Step Solution:

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Reformatting the input :

Changes made to your input should not affect the solution:

(1): "n3" was replaced by "n^3". 1 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

(27 • (m3)) - 26n3

STEP

2

:

Equation at the end of step

2

:

33m3 - 26n3

STEP

3

:

Trying to factor as a Difference of Cubes:

3.1 Factoring: 27m3-64n3

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 : 27 is the cube of 3

Check : 64 is the cube of 4

Check : m3 is the cube of m1

Check : n3 is the cube of n1

Factorization is :

(3m - 4n) • (9m2 + 12mn + 16n2)

Final result :

(3m - 4n) • (9m2 + 12mn + 16n2)

Answer 2

27 (m-2n) (m^2 + 2mn + 4n^2)