Question

factorize : (1.)4x²+y²+z²-4xy-2yz+4xz (2). 8x³+27y³+36x²y+54xy²​

Answer 1

Step-by-step explanation:

(1).

4X² + Y² + Z² - 4XY - 2YZ + 4XZ.

=> ( 2X)² + (-Y)² + (Z)² + 2 × (2X ) ( -Y ) + 2 ( -Y ) (Z ) + 2(2X ) ( Z ).

=> [ 2X + (-Y ) + Z ]² 

=> (2X - Y + Z )² . 

Answer 2

Answer:

1) 4x²+y²+z²+4xy -2yz-4xz

4x²+y²+z²+4xy -2yz-4xz=(-2x)²+(y)²+(z)² - 2(-2x)(y) -2(y)(z) +2(-2x)(z)

4x²+y²+z²+4xy -2yz-4xz=(-2x)²+(y)²+(z)² - 2(-2x)(y) -2(y)(z) +2(-2x)(z) this is in the form of,

(a-b-c)²=a²+b²+c²-2ab-2bc+2ac

(a-b-c)²=a²+b²+c²-2ab-2bc+2achere, a=-2,b=y,c=z

(a-b-c)²=a²+b²+c²-2ab-2bc+2achere, a=-2,b=y,c=z=[-2-y-z)²

2) 8x³+27y³+36x²y+54xy²

(2x)³ + (3y)³ +3(2x)²(3y) + (3)(2x) (3y)²

it's in the form of,

a³+b³+3a²b+3ab² = (a+b)³

=> (2x+3y)³