Question

Factorise: $a^2+b^2-c^2-d^2+2ab-2cd$

• A. $(a+b-c-d)(a+b+c+d)$
• B. $(a+b-c+d)(a+b+c+d)$
• C. $(a+b+c+d{)}^2$
• D. $(a-b-c+d)(a-b+c+d)$

Answer 1

The correct option is A $(a+b-c-d)(a+b+c+d)$

$a^2+b^2-c^2-d^2+2ab-2cd$
=$a^2+b^2+2ab-c^2-d^2-2cd$
=$a^2+b^2+2ab-(c^2+d^2+2cd)$
$\because x^2+y^2+2xy=(x+y{)}^2$
=$(a+b{)}^2-(c+d{)}^2$
$\because x^2-y^2=(x+y)(x-y)$
=$\left[\right(a+b)-(c+d\left)\right]\left[\right(a+b)+(c+d\left)\right]$
=$(a+b-c-d)(a+b+c+d)$