Question

Factorize:(x-y)2-10(x-y)+25
$(x - y)2 - 10(x - y) + 25$

Answer 1

Let x -y = a

a^2 - 10a + 25

= a^2 - 5a - 5a + 25

= a ( a-5) -5 ( a -5 )

= ( a -5 )( a -5)

= ( x - y -5 )( x - y - 5 )

Answer 2

The factorisation of $(x-y)^2-10(x-y)+25$ is $(x-y-5)(x-y-5)$.

Step-by-step explanation:

We have,

$(x-y)^2-10(x-y)+25$

To find, the factorisation of $(x-y)^2-10(x-y)+25=?$

Let x - y = m

∴ $a^2-10a+25$

$=a^2-2(a)(5)+5^2$

$=(a-5)^{2}$

Using identity,

$(a-b)^{2}=a^{2}-2ab+b^{2}$

$=(a-5)(a-5)$      ......(1)

Put x - y = m in equation (1), we get

$=(x-y-5)(x-y-5)$

Hence, the factorisation of $(x-y)^2-10(x-y)+25$ is $(x-y-5)(x-y-5)$.