Упр.19.3 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) a^3+8; 9) m^3 n^3+0,001;
2) c^3-64; 10) 64/343 m^3-125/216 n^3;
3) 125-b^3; 11) 8m^6+27n^9;
4) 1+x^3; 12) m^6 n^3-p^12;
5) a^3+1000; 13) 0,027x^21+0,125y^24;
6) 27a^3-1; 14) 0,216-8c^27;
7) 1000c^3-216; 15) 1000a^12 b^3+0,001c^6 d^15.
8) a^3 b^3-1;

1. $$a^3+8=a^3+2^3=(a+2)(a^2-2a+4)$$
2. $$c^3-64=c^3-4^3=(c-4)(c^2+4c+16)$$
3. $$125-b^3=5^3-b^3=(5-b)(25+5b+b^2)$$
4. $$1+x^3=1^3+x^3=(1+x)(1-x+x^2)$$
5. $$a^3+1000=a^3+10^3=(a+10)(a^2-10a+100)$$
6. $$27a^3-1=(3a)^3-1^3=(3a-1)(9a^2+3a+1)$$
7. $$1000c^3-216=(10c)^3-6^3=(10c-6)(100c^2+60c+36)$$
8. $$a^3b^3-1=(ab)^3-1^3=(ab-1)(a^2b^2+ab+1)$$
9. $$m^3n^3+0{,}001=(mn)^3+(0{,}1)^3=(mn+0{,}1)(m^2n^2-0{,}1mn+0{,}01)$$
10. $$\frac{64}{343}m^3-\frac{125}{216}n^3=\left(\frac47m\right)^3-\left(\frac56n\right)^3$$
    $$=\left(\frac47m-\frac56n\right)\left(\frac{16}{49}m^2+\frac{10}{21}mn+\frac{25}{36}n^2\right)$$
11. $$8m^6+27n^9=(2m^2)^3+(3n^3)^3$$
    $$=(2m^2+3n^3)(4m^4-6m^2n^3+9n^6)$$
12. $$m^6n^3-p^{12}=(m^2n)^3-(p^4)^3$$
    $$=(m^2n-p^4)(m^4n^2+m^2np^4+p^8)$$
13. $$0{,}027x^{21}+0{,}125y^{24}=(0{,}3x^7)^3+(0{,}5y^8)^3$$
    $$=(0{,}3x^7+0{,}5y^8)(0{,}09x^{14}-0{,}15x^7y^8+0{,}25y^{16})$$
14. $$0{,}216-8c^{27}=(0{,}6)^3-(2c^9)^3$$
    $$=(0{,}6-2c^9)(0{,}36+1{,}2c^9+4c^{18})$$
15. $$1000a^{12}b^3+0{,}001c^6d^{15}=(10a^4b)^3+(0{,}1c^2d^5)^3$$
    $$=(10a^4b+0{,}1c^2d^5)(100a^8b^2-a^4bc^2d^5+0{,}01c^4d^{10})$$

Ответ

1) $$(a+2)(a^2-2a+4)$$
2) $$(c-4)(c^2+4c+16)$$
3) $$(5-b)(25+5b+b^2)$$
4) $$(1+x)(1-x+x^2)$$
5) $$(a+10)(a^2-10a+100)$$
6) $$(3a-1)(9a^2+3a+1)$$
7) $$(10c-6)(100c^2+60c+36)$$
8) $$(ab-1)(a^2b^2+ab+1)$$
9) $$(mn+0{,}1)(m^2n^2-0{,}1mn+0{,}01)$$
10) $$\left(\frac47m-\frac56n\right)\left(\frac{16}{49}m^2+\frac{10}{21}mn+\frac{25}{36}n^2\right)$$
11) $$(2m^2+3n^3)(4m^4-6m^2n^3+9n^6)$$
12) $$(m^2n-p^4)(m^4n^2+m^2np^4+p^8)$$
13) $$(0{,}3x^7+0{,}5y^8)(0{,}09x^{14}-0{,}15x^7y^8+0{,}25y^{16})$$
14) $$(0{,}6-2c^9)(0{,}36+1{,}2c^9+4c^{18})$$
15) $$(10a^4b+0{,}1c^2d^5)(100a^8b^2-a^4bc^2d^5+0{,}01c^4d^{10})$$