Question

2. Factorise : x^2 - 2xy + y^2 - 12x + 12y + 36​

Answer 1

${x}^{2} + {y}^{2} - {6}^{2} - 2xy - 12x + 12y$

${x}^{2} + {y}^{2} - {6}^{2} + 2( - xy - 6x + 6y)$

therefore, a=x, b=-y, c=-6

from identity

${(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca)$

gives

(x-y-6) × (x-y-6) are the factors

Hope this helps

Answer 2

The factorised expression for the given expression is $(-x+y+6)(-x+y+6)$

Therefore $x^2-2xy+y^2-12x+12y+36=(-x+y+6)(-x+y+6)$

Step-by-step explanation:

Given expression is $x^2-2xy+y^2-12x+12y+36$

• To factorise the given expression :

$x^2-2xy+y^2-12x+12y+36$

Rewritting the expression as below

$=x^2+y^2+6^2-2xy-12x+12y$

$=(-x^)2+y^2+6^2+2(-x)(y)+2(y)(6)+2(6)(-x)$

$=(-x+y+6)^2$ ( by using the identity $(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca$ here a=-x,b=y and c=6 )

$=(-x+y+6)(-x+y+6)$

Therefore the factorised expression for the given expression is $(-x+y+6)(-x+y+6)$

Therefore $x^2-2xy+y^2-12x+12y+36=(-x+y+6)(-x+y+6)$