Question

How factorise 125 x cube + 27 y cube + 8 Z cube minus 90 xyz

Answer 1

ans in the attachement....

Answer 2

Answer:

The factories form of the expression is $125x^3+27y^3+8z^3-90xyz=(5x+3y+2z)(25x^2+9y^2+4z^2-15xy-6yz-10zx)$          

Step-by-step explanation:

To find : How factories $125x^3+27y^3+8z^3-90xyz$ ?

Solution :

Expression $125x^3+27y^3+8z^3-90xyz$

Using identity,

$a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$

Re-write expression as,

$(5x)^3+(3y)^3+(2z)^3-3(5x)(3y)(2z)$

Here, a=5x, b=3y and c=2z

$(5x)^3+(3y)^3+(2z)^3-3(5x)(3y)(2z)=(5x+3y+2z)((5x)^2+(3y)^2+(2z)^2-(5x)(3y)-(3y)(2z)-(2z)(5x))$

$125x^3+27y^3+8z^3-90xyz=(5x+3y+2z)(25x^2+9y^2+4z^2-15xy-6yz-10zx)$

Therefore, The factories form of the expression is $125x^3+27y^3+8z^3-90xyz=(5x+3y+2z)(25x^2+9y^2+4z^2-15xy-6yz-10zx)$