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Two factorization problems （1）xy(a^+1)+a(x^+y^）（2）xya^-(xz-y^)a-xy （3）ab(x^+y^)+xy(a^+b^）

Two factorization problems （1）xy(a^+1)+a(x^+y^）（2）xya^-(xz-y^)a-xy （3）ab(x^+y^)+xy(a^+b^）

（1）=a^xy+xy+ax^+ay^
=ax(ay+x)=y(ay+x)
=(ay+x)(ax+y)
(2) Z should be y
(3)=abx^+aby^+a^xy+b^xy
=ax(bx+ay)+by(ay+bx)
=(ax+by)(bx+ay)

1.（x+y）²-10（x+y）+25
2.a²b²/4-ab+1

1、(X+Y-5)^2
2、(ab/2-1)^2

Factorization in real numbers (by formula): x ^ 2 + XY - 3Y ^ 2

x^2 +xy - 3y^2
=x^2 +xy+y^2/4- y^2/4- 3y^2
=(x+y/2)^2-13y^2/4
=(x+y/2-√13y/2)(x+y/2+√13y/2)