Question

Разложите на множители : 2xy+x2+y2-3x-3y (5x-3)3+(3-5x)2 5x3y-5xy3 2a(x+y)+x+y 3a(m-n)-2b(n-m) 3m(p-2q)-p+2q

Answer 1

$2xy+x+y^2-3x-3y=(x^2+2xy+y^2)-(3x+3y)=\\ =(x+y)^2-3(x+y)=(x+y)(x+y-3)\\\\\\ (5x-3)^3+(3-5x)^2=(5x-3)^3+(5x-3)^2=(5x-3)^2(5x-3+1)\\ =(5x-3)(5x-2)\\\\\\ 5x^3-5xy^3=5xy(x^2-y^2)=5xy(x-y)(x+y) \\\\\\ 2a(x+y)+x+y=2a(x+y)+(x+y)=(x+y)(2a+1)\\\\\\ 2a(m-n)-2b(n-m)=3a(m-n)+2b(m-n)=(m-n)(3a+2b)\\\\\\ 3m(p-2q)-p+2q=3m(p-2q)-(p-2q)=(p-2q)(3m-1)$