Question

Factorize 125x3-216y3

Answer 1

Answer:

(5x - 6y) • (25x2 + 30xy + 36y2)

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): "y3" was replaced by "y^3". 1 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

(125 • (x3)) - (23•33y3)

STEP

2

:

Equation at the end of step

2

:

53x3 - (23•33y3)

STEP

3

:

Trying to factor as a Difference of Cubes

3.1 Factoring: 125x3-216y3

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 : 216 is the cube of 6

Check : x3 is the cube of x1

Check : y3 is the cube of y1

Factorization is :

(5x - 6y) • (25x2 + 30xy + 36y2)

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