Упр.21.35 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) x^2+2x-y^2+4y-3;
2) x^4 y^2+2x^2 y-x^2+6x-8;
3) 3x^2-4xy+y^2+4x-4.

1. $$x^2+2x-y^2+4y-3=x^2+2x+1-y^2+4y-4$$

   $$=(x+1)^2-(y^2-4y+4)=(x+1)^2-(y-2)^2$$

   $$=(x+1-y+2)(x+1+y-2)=(x-y+3)(x+y-1)$$

2. $$x^4y^2+2x^2y-x^2+6x-8=x^4y^2+2x^2y+1-x^2+6x-9$$

   $$=(x^2y+1)^2-(x^2-6x+9)=(x^2y+1)^2-(x-3)^2$$

   $$=(x^2y+1-x+3)(x^2y+1+x-3)=(x^2y-x+4)(x^2y+x-2)$$

3. $$3x^2-4xy+y^2+4x-4=4x^2-4xy+y^2-x^2+4x-4$$

   $$=(2x-y)^2-(x^2-4x+4)=(2x-y)^2-(x-2)^2$$

   $$=(2x-y-x+2)(2x-y+x-2)=(x-y+2)(3x-y-2)$$

Ответ

$$1)\ (x-y+3)(x+y-1);\quad 2)\ (x^2y-x+4)(x^2y+x-2);\quad 3)\ (x-y+2)(3x-y-2).$$