Упр.355 ГДЗ Мерзляк Полонский 7 класс (Алгебра)

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. $$(4y^3-6y+7)(-1{,}2y^3)=-4{,}8y^6+7{,}2y^4-8{,}4y^3.$$
8. $$0{,}4x^2y(3xy^2-5xy+13x^2y^3)=1{,}2x^3y^3-2x^3y^2+5{,}2x^4y^4.$$
9. $$(2{,}3a^3b-1{,}7b^4-3{,}5b)(-10a^2b)=-23a^5b^2+17a^2b^5+35a^2b^2.$$
10. $$-4pk^6(3p^2k-p+4k-2)=-12p^3k^7+4p^2k^6-16pk^7+8pk^6.$$
11. $$\frac{2}{3}mn^2(6m-1{,}8n+9)=4m^2n^2-1{,}2mn^3+6mn^2.$$
12. $$\frac{1}{7}cd\left(\frac{7}{8}c^5-\frac{7}{24}c^2d^7-\frac{1}{4}d^{10}\right)=\frac{1}{8}c^6d-\frac{1}{24}c^3d^8-\frac{1}{28}cd^{11}.$$

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. $$-12p^3k^7+4p^2k^6-16pk^7+8pk^6$$
11. $$4m^2n^2-1{,}2mn^3+6mn^2$$
12. $$\frac{1}{8}c^6d-\frac{1}{24}c^3d^8-\frac{1}{28}cd^{11}$$