Question

facrorise x²+4xy+y²

Answer 1

x2+4xy−5y2=(x−y)(x+5y)

Explanation:

x2+4xy−5y2 is a homogeneous expression. We propose that can be formed by the product of two homogeneous expresions.
x2+4xy−5y2=(ax+by)(cx+dy).
So
x2+4xy−5y2=acx2+(bc+ad)xy+bdy2
so we have
⎧⎪⎨⎪⎩1=ac4=bc+ad−5=bd
We have three equations and four incognitas. Solving for b,c,d we obtain
b=−a,c=1a

Answer 2

X2+(2XY)2+Y2

X2+2XY+Y2

Answer =X2+2XY+Y2