Question

factorize x^3(y-z)^3+y^3(z-x)^3-z^3(y-x)^3
class 9 math ncert cbse brainliest for sure
polynomial; with step by step method using identities

Answer 1

Step-by-step explanation:

x3(y-z)3+y3(z-x)3+z3(x-y)3

Final result :

-3xyz • (x2y - x2z - xy2 + xz2 + y2z - yz2)

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(((x3)•((y-z)3))+((y3)•((z-x)3)))+z3•(x-y)3

Step 2 :

Equation at the end of step 2 :

(((x3)•((y-z)3))+y3•(z-x)3)+z3•(x-y)3

Step 3 :

Equation at the end of step 3 :

(x3•(y-z)3+y3•(z-x)3)+z3•(x-y)3

Step 4 :

4.1 Evaluate : (x-y)3 = x3-3x2y+3xy2-y3

Step 5 :

Pulling out like terms :

5.1 Pull out like factors :

-3x3y2z + 3x3yz2 + 3x2y3z - 3x2yz3 - 3xy3z2 + 3xy2z3 =

-3xyz • (x2y - x2z - xy2 + xz2 + y2z - yz2)

Trying to factor by pulling out :

5.2 Factoring: x2y - x2z - xy2 + xz2 + y2z - yz2

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Answer 2

Step-by-step explanation:

Let a = x - y, b = y - z, c = z - x

Here, a + b + c = x - y + y - z + z - x = 0

Now if a + b + c = 0 then x3 + y3 + z3 = 3xyz

Hence,

(x - y)3 + (y - z)3 + (z - x)3 = 3(x - y) (y - z) (z - x).

JAI SHREE KRISHNA