Factorize the given algebraic expression. x 3+ 27y 3+ 64z 3- 36xyz
The correct answer is (x + 3y + 4z) (x 2 + 9y 2 + 16z 2 - 3xy - 12yz - 4xz).
For example, to factorize $(\text{x}-\text{y})^3 + (\text{y}-\text{z})^3 + (\text{z}-\text{x})^3$, we can observe that $(\text{x}-\text{y}) + (\text{y}-\text{z}) + (\text{z}-\text{x}) = \text{x}-\text{y}+\text{y}-\text{z}+\text{z}-\text{x} = 0$. So, the factorization is $3(\text{x}-\text{y})(\text{y}-\text{z})(\text{z}-\text{x})$. Recognizing the standard forms of algebraic expressions and knowing the corresponding identities is crucial for efficient factorization. Always try to see if the expression fits one of the known identity patterns before attempting other factorization methods.
Similar Questions
Which of the following numbers is divisible by 12?
How many such numbers are there from 500 to 750 (including both) which are neither divisible by 3 nor by 11?
If the number 756534P57Q is divisible by 72, then find the value of 2P + Q.
The six-digit number 7x1yyx is a multiple of 33 for non-zero digits x and y. Which of the following could be a possible value of (x + y)?
Find the least value of ‘@’ to make the number 7@5471 perfectly divisible by 9.
What is the least value of * so that the number 457643*4 is divisible by 18?
Which of the following is NOT divisible by 4?
Which of the following numbers will completely divide (661 + 662 + 663 + 664)?
Which of the following is perfectly divisible by 11?
Find the least value of K for which 7864K3 is divisible by 7.
Important Questions from Multiples and Factors
- How many factors of $2^{2} \times 3^{1} \times 5^{2} \times 7^{1}$ are divisible by 50 but not by 100?
- What is the total number of odd and even divisors of 120, respectively?
- The Government of India Constituted Narcotics Control Bureau in _____.
- The least number by which 294 must be multiplied to make it a perfect square, is:
Which of the following numbers is divisible by 12?
