Question

ax + a2x + aby + by- (ax + by)^2
Factorise it please
The answer is :-
(ax+by)(1+a-ax-by)​

Answer 1

(ax+by)+a²x+ aby -(ax+by)². { arrange it like these}

(ax+by)+a(ax+by) -(ax+ by)²

(ax+by)[1+a -(ax+by)]. { taking (ax+by) common}

(ax+by)(1+a-ax-by)

Answer 2

The factorisation of $ax+a^2x+aby+by-(ax+by)^2=(ax+by)(1+a-ax-by)$

Step-by-step explanation:

We have,

$ax+a^2x+aby+by-(ax+by)^2$

To find, the factorisation of $ax+a^2x+aby+by-(ax+by)^2=?$

∴ $ax+a^2x+aby+by-(ax+by)^2$

$=(ax+by)+a^2x+ aby-(ax+by)^2$

$=(ax+by)+a(ax+by)-(ax+ by)^2$

Take (ax+by) as common, we get

$=(ax+by)[1+a -(ax+by)]$

$=(ax+by)(1+a-ax-by)$

The factorisation of $ax+a^2x+aby+by-(ax+by)^2=(ax+by)(1+a-ax-by)$

Hence, the factorisation of $ax+a^2x+aby+by-(ax+by)^2=(ax+by)(1+a-ax-by)$