Упр.21.28 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) x^2-4x+3; 4) x^2+x-6;
2) a^2+2a-24; 5) c^2+8cd+15d^2;
3) y^2+12y+35; 6) 9x^2-30xy+16y^2.

1. $$x^2-4x+3=x^2-4x+4-1=(x-2)^2-1=(x-2-1)(x-2+1)=(x-3)(x-1).$$
2. $$a^2+2a-24=a^2+2a+1-25=(a+1)^2-5^2=(a+1-5)(a+1+5)=(a-4)(a+6).$$
3. $$y^2+12y+35=y^2+12y+36-1=(y+6)^2-1=(y+6-1)(y+6+1)=(y+5)(y+7).$$
4. $$x^2+x-6=x^2+2\cdot \frac12 x+\frac14-\frac14-6=\left(x+\frac12\right)^2-\frac{25}{4}$$
   $$=\left(x+\frac12-\frac52\right)\left(x+\frac12+\frac52\right)=\left(x-2\right)\left(x+3\right).$$
5. $$c^2+8cd+15d^2=c^2+8cd+16d^2-d^2=(c+4d)^2-d^2$$
   $$=(c+4d-d)(c+4d+d)=(c+3d)(c+5d).$$
6. $$9x^2-30xy+16y^2=9x^2-30xy+25y^2-9y^2=(3x-5y)^2-(3y)^2$$
   $$=(3x-5y-3y)(3x-5y+3y)=(3x-8y)(3x-2y).$$

Ответ

1) $$(x-3)(x-1)$$
2) $$(a-4)(a+6)$$
3) $$(y+5)(y+7)$$
4) $$(x-2)(x+3)$$
5) $$(c+3d)(c+5d)$$
6) $$(3x-8y)(3x-2y)$$