Разложить ** множители. 1) x-y+√(x-y) 2) 5x-5y-7√(x-y) 3) √(x^2-y^2)+√(x-y) 4)...

Question

Разложить на множители.

1) x-y+√(x-y)

2) 5x-5y-7√(x-y)

3) √(x^2-y^2)+√(x-y)

4) st+t√t+s√s+√(st)

Answer 1

x-y+√(x-y)=sqrt(x-y)(sqrt(x-y)-1)

5x-5y-7sqrt(x-y)=5(x-y)-7sqrt(x-y)=sqrt(x-y)(5sqrt(x-y)-7)

sqrt*x^2-y^2)+sqrt(x-y)=sqrt((x-y)*(x+y))+sqrt(x-y)=sqrt(x-y)(sqrt(x+y)+1)

st+tsqrt(t)+ssqrt(s)+sqrt(st)=s(t+sqrt(s))+sqrt(t)(t+sqrt(s))=(t+sqrt(s))*(s+sqrt(t))

Answer 2

Решение:

1)x-y+√(x-y)=√(x-y)(√(x-y)-1)

2)5x-5y-7√(x-y)=5(x-y)-7√(x-y)=√(x-y)(5√(x-y)-7)

3)√x²-y²)+√(x-y)=√((x-y)*(x+y))+√x-y)=√(x-y)(√(x+y)+1)

4)st+t√t+√s+√st=s(t+s√s)+√t(t+√s)=(t+√s)*(s+√t)