Упр.103 Вариант 3 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) (x+5)(y-7); 7) (-2-y)(y^2 +3);
2) (x-1)(x+5); 8) (3a^2 — b)(4a^2 +3b);
3) (3x-5)(2x+7); 9) (a-3)(a^2 + 4a+2);
4) (5x^2 -1)(5x+1); 10) (y-2z)(y^2 -2yz-5z^2);
5) (5m-2n)(3m+n); 11) m(2m-1)(3m+2);
6) (4x^2 -x)(2x^2 +3x); 12) -6x^2 (4-2x)(3x^2 +11x).

1. $$\begin{aligned} (x+5)(y-7) &= xy-7x+5y-35 \end{aligned}$$
2. $$\begin{aligned} (x-1)(x+5) &= x^2+5x-x-5 \\ &= x^2+4x-5 \end{aligned}$$
3. $$\begin{aligned} (3x-5)(2x+7) &= 6x^2+21x-10x-35 \\ &= 6x^2+11x-35 \end{aligned}$$
4. $$\begin{aligned} (5x^2-1)(5x+1) &= 25x^3+5x^2-5x-1 \end{aligned}$$
5. $$\begin{aligned} (5m-2n)(3m+n) &= 15m^2+5mn-6mn-2n^2 \\ &= 15m^2-mn-2n^2 \end{aligned}$$
6. $$\begin{aligned} (4x^2-x)(2x^2+3x) &= 8x^4+12x^3-2x^3-3x^2 \\ &= 8x^4+10x^3-3x^2 \end{aligned}$$
7. $$\begin{aligned} (-2-y)(y^2+3) &= -2y^2-6-y^3-3y \\ &= -y^3-2y^2-3y-6 \end{aligned}$$
8. $$\begin{aligned} (3a^2-b)(4a^2+3b) &= 12a^4+9a^2b-4a^2b-3b^2 \\ &= 12a^4+5a^2b-3b^2 \end{aligned}$$
9. $$\begin{aligned} (a-3)(a^2+4a+2) &= a^3+4a^2+2a-3a^2-12a-6 \\ &= a^3+a^2-10a-6 \end{aligned}$$
10. $$\begin{aligned} (y-2z)(y^2-2yz-5z^2) &= y^3-2y^2z-5yz^2-2y^2z+4yz^2+10z^3 \\ &= y^3-4y^2z-yz^2+10z^3 \end{aligned}$$
11. $$\begin{aligned} m(2m-1)(3m+2) &= m(6m^2+4m-3m-2) \\ &= m(6m^2+m-2) \\ &= 6m^3+m^2-2m \end{aligned}$$
12. $$\begin{aligned} -6x^2(4-2x)(3x^2+11x) &= -6x^2(12x^2+44x-6x^3-22x^2) \\ &= -6x^2(-6x^3-10x^2+44x) \\ &= 36x^5+60x^4-264x^3 \end{aligned}$$

Ответ

1) $$xy-7x+5y-35$$;
2) $$x^2+4x-5$$;
3) $$6x^2+11x-35$$;
4) $$25x^3+5x^2-5x-1$$;
5) $$15m^2-mn-2n^2$$;
6) $$8x^4+10x^3-3x^2$$;
7) $$-y^3-2y^2-3y-6$$;
8) $$12a^4+5a^2b-3b^2$$;
9) $$a^3+a^2-10a-6$$;
10) $$y^3-4y^2z-yz^2+10z^3$$;
11) $$6m^3+m^2-2m$$;
12) $$36x^5+60x^4-264x^3$$.