Question

factorise 1) 64x^3+27y^3+z^3-36xyz 2) 27a^2+125b^3+135a^2b+225ab^2

Answer 1

Hello friends!!

Here is your answer :

Ans 1

$64 {x}^{3} + {27y}^{3} + {z}^{3} - 36xyz$

${(4x)}^{3} + {(3y)}^{3} + {(z)}^{3} - 3(4x)(3y)(z)$

Using identity :

a³ + b³ + c³ - 3abc = ( a + b + c) (a² + b² + c² - ab - bc - ca)


a = 4x , b = 7y , c = z

$= > (4x + 7y + z)( {(4x)}^{2} + {(7y)}^{2} + {(z)}^{2} - (4x)(7y) - (7y)(z) - (z)(4x)$


$= > (4x + 7y + z)(16 {x}^{2} + {9y}^{2} + {z}^{2} - 28xy - 7yz - 4xz$

__________


Ans 2

$27 {a}^{3} + {125b}^{3} + 135 {a}^{2} b + 225 a{b}^{2}$

${(3a)}^{3} + {(5b)}^{3} + 3(3a)(5y)(3a + 5y)$


Using identity :

( x + y)³ = x³ + y³ + 3xy( x + y )


x = 3a , y = 5b

$= > {(3a + 5b)}^{3}$


$= > (3a + 5b)(3a + 5b)(3a + 5b)$

Hope it helps you. ☺️☺️☺️☺️

# Be Brainly