Упр.13.10 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) c(x-3)-d(x-3); 2) m(p-k)-(p-k);
3) m(x-y)-n(y-x); 4) x(2-x)+4(x-2);
5) 4x(2x-y)-5y(y-2x); 6) (y+1)^2-4y(y+1);
7) 10(a^2-5)+(a^2-5)^2; 8) (a-2)^2-6(a-2).

1. $$c(x-3)-d(x-3)=(x-3)(c-d)$$
2. $$m(p-k)-(p-k)=(p-k)(m-1)$$
3. $$m(x-y)-n(y-x)=m(x-y)+n(x-y)=(x-y)(m+n)$$
4. $$x(2-x)+4(x-2)=x(2-x)-4(2-x)=(2-x)(x-4)$$
5. $$4x(2x-y)-5y(y-2x)=4x(2x-y)+5y(2x-y)=(2x-y)(4x+5y)$$
6. $$(y+1)^2-4y(y+1)=(y+1)\bigl((y+1)-4y\bigr)=(y+1)(1-3y)$$
7. $$10(a^2-5)+(a^2-5)^2=(a^2-5)\bigl(10+(a^2-5)\bigr)=(a^2-5)(a^2+5)$$
8. $$(a-2)^2-6(a-2)=(a-2)\bigl((a-2)-6\bigr)=(a-2)(a-8)$$

Ответ

1. $$ (x-3)(c-d) $$
2. $$ (p-k)(m-1) $$
3. $$ (x-y)(m+n) $$
4. $$ (2-x)(x-4) $$
5. $$ (2x-y)(4x+5y) $$
6. $$ (y+1)(1-3y) $$
7. $$ (a^2-5)(a^2+5) $$
8. $$ (a-2)(a-8) $$