Упр.11.1 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) 3x(2x+5);
2) 4x(x^2-8x-2);
3)-2a(a^2+a-3);
4) 5b^2 (3b^2-7b+10);
5) mn(m^2 n-n^3 );
6) 2ab(a^3-3a^2 b+b^2 );
7) (4y^3-6y+7)•(-1,2y^3 );
8) 0,4x^2 y(3xy^2-5xy+13x^2 y^3 );
9) (2,3a^3 b-1,7b^4-3,5b)•(-10a^2 b);
10)-4pk^3 (3p^2 k-p+4k-2);
11) 2/3 mn^2 (6m-1,8n+9);
12) 1 1/7 cd(7/8 c^5-7/24 c^2 d^7-1/4 d^10 ).

1. $$3x(2x+5)=3x\cdot 2x+3x\cdot 5=6x^2+15x$$
2. $$4x(x^2-8x-2)=4x\cdot x^2-4x\cdot 8x-4x\cdot 2=4x^3-32x^2-8x$$
3. $$-2a(a^2+a-3)=-2a\cdot a^2-2a\cdot a+(-2a)\cdot(-3)=-2a^3-2a^2+6a$$
4. $$5b^2(3b^2-7b+10)=5b^2\cdot 3b^2-5b^2\cdot 7b+5b^2\cdot 10=15b^4-35b^3+50b^2$$
5. $$mn(m^2n-n^3)=mn\cdot m^2n-mn\cdot n^3=m^3n^2-mn^4$$
6. $$2ab(a^3-3a^2b+b^2)=2ab\cdot a^3-2ab\cdot 3a^2b+2ab\cdot b^2=2a^4b-6a^3b^2+2ab^3$$
7. $$(4y^3-6y+7)\cdot(-1{,}2y^3)=-1{,}2y^3\cdot 4y^3+(-1{,}2y^3)\cdot(-6y)+(-1{,}2y^3)\cdot 7$$
   $$=-4{,}8y^6+7{,}2y^4-8{,}4y^3$$
8. $$0{,}4x^2y(3xy^2-5xy+13x^2y^3)=0{,}4x^2y\cdot 3xy^2-0{,}4x^2y\cdot 5xy+0{,}4x^2y\cdot 13x^2y^3$$
   $$=1{,}2x^3y^3-2x^3y^2+5{,}2x^4y^4$$
9. $$(2{,}3a^3b-1{,}7b^4-3{,}5b)\cdot(-10a^2b)$$
   $$=-23a^5b^2+17a^2b^5+35a^2b^2$$
10. $$-4pk^3(3p^2k-p+4k-2)=-4pk^3\cdot 3p^2k-4pk^3\cdot(-p)-4pk^3\cdot 4k-4pk^3\cdot(-2)$$
    $$=-12p^3k^4+4p^2k^3-16pk^4+8pk^3$$
11. $$\frac{2}{3}mn^2(6m-1{,}8n+9)=\frac{2}{3}mn^2\cdot 6m-\frac{2}{3}mn^2\cdot 1{,}8n+\frac{2}{3}mn^2\cdot 9$$
    $$=4m^2n^2-1{,}2mn^3+6mn^2$$
12. $$1\frac{1}{7}cd\left(\frac{7}{8}c^5-\frac{7}{24}c^2d^7-\frac{1}{4}d^{10}\right)=\frac{8}{7}cd\left(\frac{7}{8}c^5-\frac{7}{24}c^2d^7-\frac{1}{4}d^{10}\right)$$
    $$=c^6d-\frac{1}{3}c^3d^8-\frac{2}{7}cd^{11}$$

Ответ

1) $$6x^2+15x$$;
2) $$4x^3-32x^2-8x$$;
3) $$-2a^3-2a^2+6a$$;
4) $$15b^4-35b^3+50b^2$$;
5) $$m^3n^2-mn^4$$;
6) $$2a^4b-6a^3b^2+2ab^3$$;
7) $$-4{,}8y^6+7{,}2y^4-8{,}4y^3$$;
8) $$1{,}2x^3y^3-2x^3y^2+5{,}2x^4y^4$$;
9) $$-23a^5b^2+17a^2b^5+35a^2b^2$$;
10) $$-12p^3k^4+4p^2k^3-16pk^4+8pk^3$$;
11) $$4m^2n^2-1{,}2mn^3+6mn^2$$;
12) $$c^6d-\frac{1}{3}c^3d^8-\frac{2}{7}cd^{11}$$.