Question

x^2-y^2-8yz-16z^2 factorise ​

Answer 1

x2-y2+8yz-16z2

Final result :

 x2 - y2 + 8yz - 16z2

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (((x2) -  (y2)) +  8yz) -  24z2

Step  2  :

Final result :

 x2 - y2 + 8yz - 16z2

Answer 2

The factorisation of $x^2-y^2-8yz-16z^2$ is (x + y)(x - y) - 8z(y + 2z).

Step-by-step explanation:

We have,

$x^2-y^2-8yz-16z^2$

To find, the factorisation of $x^2-y^2-8yz-16z^2$ = ?

∴ $x^2-y^2-8yz-16z^2$

= $(x^2-y^2)-(8yz+16z^2)$

Using the algebraic identity,

$a^2-b^2$ = (a + b)(a - b)

= $(x+y)(x-y)-(8yz+16z^2)$

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

∴ The factorisation of $x^2-y^2-8yz-16z^2$ = (x + y)(x - y) - 8z(y + 2z)

Thus, the factorisation of $x^2-y^2-8yz-16z^2$ is (x + y)(x - y) - 8z(y + 2z).