Question

Factorise
x2-y2-2yz-z2

Answer 1

bu using formulae we have to solve

Answer 2

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

Solution:

Given that, we have to factorize:

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

Group the above expression

$x^2 - (y^2 +2yz +z^2)$

We know that,

$(a + b)^2 = a^2 + b^2 + 2ab\\\\Therefore\\\\y^2 + 2yz +z^2 = (y+z)^2$

$Thus\ the\ equation\ becomes\\\\x^2 - (y + z)^2\\\\We\ know\ that\\\\a^2 - b^2 = (a+b)(a - b)\\\\Therefore\\\\(x + y + z)(x - y - z)$

Thus the given expression is factored

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