Question

Factorise $(1-x^2)(1-y^2)+4xy$ is _____

• A. $(1+yx+x+y)(1+xy-x+y)$
• B. $=(1+yx+x-y)(1+xy-x-y)$
• C. $=(1+yx+x-y)(1+xy-x^2-y^2)$
• D. $=(1-y^{2}x+x-y)(1+xy-x-y)$

Answer 1

The correct option is B $=(1+yx+x-y)(1+xy-x-y)$

$(1-x^2)(1-y^2)+4xy$
$=1-y^2-x^2+x^2{y}^2+4xy$
By rearranging the terms
$=1+x^2{y}^2+2xy-x^2-y^2+2xy$
$=(1+x^2{y}^2+2xy)-(x^2+y^2-2xy)$
$=(1+xy{)}^2-(x-y{)}^2$
{ $a^2-b^2=(a+b)(a-b)$ }
$=(1+yx+x-y)(1+xy-x-y)$