Question

factorize the following x3+64y3+z3-12xyz​

Answer 1

Step-by-step explanation:

Find an answer to your question Factorise the polynomial x3 + 8y3 + 64 z3 – 24xyz.

Answer 2

The answer to the factorisation is (x+4y+z) (x²+16y²+z²-4xy-4yz-zx)

Given : The given mathematical expression is, x³+64y³+z³-12xyz

To find :

To find :Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to factorise the given expression)

Here, we will be using general algebraic identities.

So,

= x³+64y³+z³-12xyz

= (x)³ + (4y)³ + (z)³ - (3 × x × 4y × z)

Now, we know that :

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

Here,

• a = x
• b = 4y
• c = z

So, the further steps of the factorisation will be :

= (x)³ + (4y)³ + (z)³ - (3 × x × 4y × z)

= (x+4y+z) [(x)² + (4y)² + (z)² -(x × 4y) - (4y × z) - (z × x)]

= (x+4y+z) (x²+16y²+z²-4xy-4yz-zx)

(This will be considered as the final result.)

Hence, the answer to the factorisation is (x+4y+z) (x²+16y²+z²-4xy-4yz-zx)