Question

Разложите многочлен на множители:
1. 7x^2+5xy-12y^2
2. 2x^2-7xy+5y^2-3x+3y
3. x^4+4y^4

Answer 1

$1)7x^2+5xy-12y^2=\7x^2-7xy+12xy-12y^2=\7x(x-y)+12y(x-y)=\(x-y)(7x+12y)\ 2)\ 2x^2-7xy+5y^2-3x+3y=\ 2x^2-7xy+7y^2-2y^2-3(x-y)=\ 2(x-y)(x+y)-7y(x-y)-3(x-y)=\ (x-y)(2x-5y-3) \ 3)\ x^4+4y^4=(x^2)^2+(2y^2)^2\ (x^2+2y^2)-4x^2y^2=\ (x^2+2y^2)-(2xy)^2=(x^2+2y^2-2xy)(x^2+2y^2+2xy)$