Question

Factorize :
$x {}^{2} - 10xy + 16y {}^{2} - z {}^{2} + 6yz$

Answer 1

Final Answer : (x-2y-z) (x-8y+z)

Steps:
1)
${x}^{2} - 10xy + 16 {y}^{2} - {z}^{2} + 6yz \\ = { x}^{2} - 10xy + 25 {y}^{2} - 9 {y}^{2} - {z}^{2} \\ + 6yz \\ = {(x - 5y)}^{2} - ( {z}^{2} - 6yz + 9 {y}^{2} ) \\ = {(x - 5y)}^{2} - {(z - 3y)}^{2} \\ = (x - 5y - z + 3y) \\ \times ( x - 5y + z - 3y) \\ = (x - 2y - z)(x - 8y + z)$