Упр.13.9 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1. 13.9. Разложите на множители:
   1. $$2x(a+b)+y(a+b)$$;
   2. $$(a-4)-b(a-4)$$;
   3. $$5a(m-n)+7b(m-n)$$;
   4. $$6x(4x+1)-11(4x+1)$$;
   5. $$a(c-d)+b(d-c)$$;
   6. $$x(x-6)-10(6-x)$$;
   7. $$b(b-20)+(20-b)$$;
   8. $$6a(a-3b)-13b(3b-a)$$;
   9. $$(m-9)^2-3(m-9)$$;
   10. $$a(a+5)^2+(a+5)$$;
   11. $$(m^2-3)-n(m^2-3)^2$$;
   12. $$8c(p-12)+7d(p-12)^2$$.

1. $$2x(a+b)+y(a+b)=(a+b)(2x+y)$$
2. $$\begin{aligned} (a-4)-b(a-4)&=(a-4)-b(a-4)\\ &=(a-4)(1-b) \end{aligned}$$
3. $$5a(m-n)+7b(m-n)=(m-n)(5a+7b)$$
4. $$6x(4x+1)-11(4x+1)=(4x+1)(6x-11)$$
5. $$\begin{aligned} a(c-d)+b(d-c)&=a(c-d)-b(c-d)\\ &=(c-d)(a-b) \end{aligned}$$
6. $$\begin{aligned} x(x-6)-10(6-x)&=x(x-6)+10(x-6)\\ &=(x-6)(x+10) \end{aligned}$$
7. $$\begin{aligned} b(b-20)+(20-b)&=b(b-20)-(b-20)\\ &=(b-20)(b-1) \end{aligned}$$
8. $$\begin{aligned} 6a(a-3b)-13b(3b-a)&=6a(a-3b)+13b(a-3b)\\ &=(a-3b)(6a+13b) \end{aligned}$$
9. $$\begin{aligned} (m-9)^2-3(m-9)&=(m-9)\bigl((m-9)-3\bigr)\\ &=(m-9)(m-12) \end{aligned}$$
10. $$\begin{aligned} a(a+5)^2+(a+5)&=(a+5)\bigl(a(a+5)+1\bigr)\\ &=(a+5)(a^2+5a+1) \end{aligned}$$
11. $$\begin{aligned} (m^2-3)-n(m^2-3)^2&=(m^2-3)\bigl(1-n(m^2-3)\bigr)\\ &=(m^2-3)(1-m^2n+3n) \end{aligned}$$
12. $$\begin{aligned} 8c(p-12)+7d(p-12)^2&=(p-12)\bigl(8c+7d(p-12)\bigr)\\ &=(p-12)(8c+7pd-84d) \end{aligned}$$

Ответ

1) $$(a+b)(2x+y)$$
2) $$(a-4)(1-b)$$
3) $$(m-n)(5a+7b)$$
4) $$(4x+1)(6x-11)$$
5) $$(c-d)(a-b)$$
6) $$(x-6)(x+10)$$
7) $$(b-20)(b-1)$$
8) $$(a-3b)(6a+13b)$$
9) $$(m-9)(m-12)$$
10) $$(a+5)(a^2+5a+1)$$
11) $$(m^2-3)(1-m^2n+3n)$$
12) $$(p-12)(8c+7pd-84d)$$