Упр.103 Вариант 2 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

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

1. $$\begin{aligned}
   (a+2)(b-3) &= ab-3a+2b-6
   \end{aligned}$$
2. $$\begin{aligned}
   (m-4)(m+5) &= m^2+5m-4m-20 \\
   &= m^2+m-20
   \end{aligned}$$
3. $$\begin{aligned}
   (3x-1)(2x+5) &= 6x^2+15x-2x-5 \\
   &= 6x^2+13x-5
   \end{aligned}$$
4. $$\begin{aligned}
   (3b^2+2)(2b-4) &= 6b^3-12b^2+4b-8
   \end{aligned}$$
5. $$\begin{aligned}
   (4x-y)(2x-3y) &= 8x^2-12xy-2xy+3y^2 \\
   &= 8x^2-14xy+3y^2
   \end{aligned}$$
6. $$\begin{aligned}
   (3a^2+a)(5a^2-2a) &= 15a^4-6a^3+5a^3-2a^2 \\
   &= 15a^4-a^3-2a^2
   \end{aligned}$$
7. $$\begin{aligned}
   (-x-2)(2x^3-3) &= -2x^4+3x-4x^3+6 \\
   &= -2x^4-4x^3+3x+6
   \end{aligned}$$
8. $$\begin{aligned}
   (3a^2-5b)(5a^2+b) &= 15a^4+3a^2b-25a^2b-5b^2 \\
   &= 15a^4-22a^2b-5b^2
   \end{aligned}$$
9. $$\begin{aligned}
   (y+3)(y^2-2y+5) &= y^3-2y^2+5y+3y^2-6y+15 \\
   &= y^3+y^2-y+15
   \end{aligned}$$
10. $$\begin{aligned}
    (m+3n)(m^2-6mn-n^2) &= m^3-6m^2n-mn^2+3m^2n-18mn^2-3n^3 \\
    &= m^3-3m^2n-19mn^2-3n^3
    \end{aligned}$$
11. $$\begin{aligned}
    2x(3x-1)(2x+5) &= 2x(6x^2+15x-2x-5) \\
    &= 2x(6x^2+13x-5) \\
    &= 12x^3+26x^2-10x
    \end{aligned}$$
12. $$\begin{aligned}
    -3x^2(2-3x)(3x^2+11x) &= -3x^2(6x^2+22x-9x^3-33x^2) \\
    &= -3x^2(-9x^3-27x^2+22x) \\
    &= 27x^5+81x^4-66x^3
    \end{aligned}$$

Ответ

1) $$ab-3a+2b-6$$;
2) $$m^2+m-20$$;
3) $$6x^2+13x-5$$;
4) $$6b^3-12b^2+4b-8$$;
5) $$8x^2-14xy+3y^2$$;
6) $$15a^4-a^3-2a^2$$;
7) $$-2x^4-4x^3+3x+6$$;
8) $$15a^4-22a^2b-5b^2$$;
9) $$y^3+y^2-y+15$$;
10) $$m^3-3m^2n-19mn^2-3n^3$$;
11) $$12x^3+26x^2-10x$$;
12) $$27x^5+81x^4-66x^3$$.