Question

factorize х^3 + 216y^3​

Answer 1

Step-by-step explanation:

${x}^{3} + 216 {y}^{3} = {x}^{3} + {(6y)}^{3} \\ = (x + 6y)( {x}^{2} - 6xy + 36 {y}^{2} )$

Answer 2

HERE IS THE ANSWER....

Theory : A difference of two perfect cubes, a3 - b3 can be factored into

Theory : A difference of two perfect cubes, a3 - b3 can be factored into (a-b) • (a2 +ab +b2)

Proof : (a-b)•(a2+ab+b2) =

Proof : (a-b)•(a2+ab+b2) = a3+a2b+ab2-ba2-b2a-b3 =

Proof : (a-b)•(a2+ab+b2) = a3+a2b+ab2-ba2-b2a-b3 = a3+(a2b-ba2)+(ab2-b2a)-b3 =

Proof : (a-b)•(a2+ab+b2) = a3+a2b+ab2-ba2-b2a-b3 = a3+(a2b-ba2)+(ab2-b2a)-b3 = a3+0+0+b3 =

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 : 216 is the cube of 6

Check : x3 is the cube of x1

Check : y3 is the cube of y1

Factorization is :

(x - 6y) • (x2 + 6xy + 36y2)