Question

54x^3-250y^3 factorise

Answer 1

Hey friend, Harish here.

Here is your answer:

$54x^3-250y^3$

⇒ $2(27x^3 - 125y^3)$

⇒ $2 \left [(3x)^3 - (5y)^3 \right ]$

We know that,  a³ - b³ = (a - b)(a² + ab + b²)

⇒ $2(3x - 5y) \left [(3x)^2 + (3x)(5y) + (5x)^2 \right ]$

⇒ $2(3x-5y)(9x^2 +15xy + 25y^2)$
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Hope my answer is helpful to you.

Answer 2

STEP

1

:

Equation at the end of step 1

 (54 • (a3)) -  (2•53b3)

STEP  

2

:

Equation at the end of step

2

:

 (2•33a3) -  (2•53b3)

STEP

3

:

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  54a3 - 250b3  =   2 • (27a3 - 125b3)  

Trying to factor as a Difference of Cubes:

4.2      Factoring:  27a3 - 125b3  

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 :  125  is the cube of   5  

Check :  a3 is the cube of   a1

Check :  b3 is the cube of   b1

Factorization is :

            (3a - 5b)  •  (9a2 + 15ab + 25b2)