Question

X²-10xy + 16y²-z² + 6yz​

Answer 1

Answer:

(x - 8y + z)(x - 2y - z)

Step-by-step explanation:

Factorize :

x²-10xy + 16y²-z² + 6yz​

Solution:

x²-10xy + 16y²-z² + 6yz​

Firstly, make sure that all the terms are arranged in a well ordered manner:

x²-10xy + 16y²-z² + 6yz​

Secondly, split the term (16y²) common to both equation:

(x²-10xy + 25y²) - 9y² -z² + 6yz​

Thirdly, factorize both terms:

(x - 5y)² - 1(z² - 6yz + 9y²)

Factorizing the second term:

(x - 5y)² - (z - 3y)²

Using the difference of two squares, that is A² - B² = (A + B)(A - B):

(x - 5y)² - (z - 3y)² = [(x - 5y) + (z - 3y)][(x - 5y) - (z - 3y)]

= [x - 5y + z - 3y][x - 5y - z + 3y]

= (x - 8y + z)(x - 2y - z)