Question

factorise
x^2+2xy+y^2-z^2​

Answer 1

Given equation is,

$x^{2} +2xy+y^{2}-z^{2}$

From the equation $x^{2} +2xy+y^{2}$ can be written as $(x+y)^{2}$

So, replace $x^{2} +2xy+y^{2}$ with $(x+y)^{2}$

$(x+y)^{2}-z^{2}$

The equation is similar to $a^{2} -b^{2}=(a+b)(a-b)$

$a=x+y$

$b=z$

So, it can be written as $(x+y+z)(x+y-z)$

Therefore, $x^{2} +2xy+y^{2}-z^{2}$ factorization is $(x+y+z)(x+y-z)$.

Answer 2

Answer:

$(x+y+z)(x+y-z)$

Step-by-step explanation:

• Given expression,

$x^{2}+2xy+y^{2}-z{2}$

• As we know, $(a+b)^{2}=a^{2}+2ab+b^{2}$

$=(x+y)^{2}-z^{2}$

• The above expression is in the form of  $a^{2}-b^{2}=(a+b)(a-b)$, where $a=x+y$ and $b=z$

$=(x+y+z)(x+y-z)$.

Hence, the expression $x^{2}+2xy+y^{2}-z{2}$ can be written as $=(x+y+z)(x+y-z)$.