Упр.355 ГДЗ Муравин 7 класс (Алгебра)

Разложите на множители выражение:

1. а) $$a(b+c)+3(b+c)$$;
   б) $$y(a-c)+5a-5c$$;
   в) $$k(-a+b)-2a+2b$$;
   г) $$(c-k)-c+k$$;
   д) $$p-q+a(p-q)$$;
   е) $$c-4p-n(c-4p)$$;
   ж) $$xy-x^2+3(x-y)$$;
   з) $$q(n-c)-pn+pc$$;
   и) $$(a-b)^2-7(a-b)$$;
   к) $$x-y+(x-y)^2$$;
   л) $$bx+by-(x+y)^2$$;
   м) $$(p-k)^2-py+ky$$.

1. $$a(b+c)+3(b+c)=(b+c)(a+3)$$
2. $$y(a-c)+5a-5c=y(a-c)+5(a-c)=(a-c)(y+5)$$
3. $$k(-a+b)-2a+2b=-k(a-b)-2(a-b)=(a-b)(-k-2)=-(a-b)(k+2)=(b-a)(k+2)$$
4. $$\begin{aligned} (c-k)-c+k&=(c-k)-(c-k)\\ &=0 \end{aligned}$$
5. $$p-q+a(p-q)=(p-q)+a(p-q)=(p-q)(1+a)$$
6. $$c-4p-n(c-4p)=(c-4p)-n(c-4p)=(c-4p)(1-n)$$
7. $$\begin{aligned} xy-x^2+3(x-y)&=x(y-x)-3(y-x)\\ &=(y-x)(x-3) \end{aligned}$$
8. $$q(n-c)-pn+pc=q(n-c)-p(n-c)=(n-c)(q-p)$$
9. $$\begin{aligned} (a-b)^2-7(a-b)&=(a-b)(a-b)-7(a-b)\\ &=(a-b)(a-b-7) \end{aligned}$$
10. $$\begin{aligned} x-y+(x-y)^2&=(x-y)+(x-y)(x-y)\\ &=(x-y)\bigl(1+x-y\bigr) \end{aligned}$$
11. $$\begin{aligned} bx+by-(x+y)^2&=b(x+y)-(x+y)(x+y)\\ &=(x+y)(b-x-y) \end{aligned}$$
12. $$\begin{aligned} (p-k)^2-py+ky&=(p-k)^2-y(p-k)\\ &=(p-k)(p-k)-y(p-k)\\ &=(p-k)(p-k-y) \end{aligned}$$

Ответ

1) $$(b+c)(a+3)$$
2) $$(a-c)(y+5)$$
3) $$(b-a)(k+2)$$
4) $$0$$
5) $$(p-q)(1+a)$$
6) $$(c-4p)(1-n)$$
7) $$(y-x)(x-3)$$
8) $$(n-c)(q-p)$$
9) $$(a-b)(a-b-7)$$
10) $$(x-y)(1+x-y)$$
11) $$(x+y)(b-x-y)$$
12) $$(p-k)(p-k-y)$$