Упр.16.4 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) b^2-d^2; 7) 900-81k^2; 13) a^2 b^2 c^2-1;
2) x^2-1; 8) 16x^2-121y^2; 14) 100a^2-0,01b^2;
3) -x^2+1; 9) b^2 c^2-1; 15) a^4-b^2;
4) 36-c^2; 10) 1/4 x^2-1/9 y^2; 16) p^2 t^2-0,36k^2 d^2;
5) 4-25a^2; 11) -4a^2 b^2+25; 17) y^10-9;
6) 49a^2-100; 12) 144x^2 y^2-400; 18) 4x^12-1 11/25 y^16.

1. $$b^2-d^2=(b-d)(b+d)$$
2. $$x^2-1=(x-1)(x+1)$$
3. $$-x^2+1=1-x^2=(1-x)(1+x)$$
4. $$36-c^2=(6-c)(6+c)$$
5. $$4-25a^2=(2-5a)(2+5a)$$
6. $$49a^2-100=(7a-10)(7a+10)$$
7. $$900-81k^2=(30-9k)(30+9k)$$
8. $$16x^2-121y^2=(4x-11y)(4x+11y)$$
9. $$b^2c^2-1=(bc-1)(bc+1)$$
10. $$\frac14x^2-\frac19y^2=\left(\frac12x-\frac13y\right)\left(\frac12x+\frac13y\right)$$
11. $$-4a^2b^2+25=25-4a^2b^2=(5-2ab)(5+2ab)$$
12. $$144x^2y^2-400=(12xy-20)(12xy+20)$$
13. $$a^2b^2c^2-1=(abc-1)(abc+1)$$
14. $$100a^2-0{,}01b^2=(10a-0{,}1b)(10a+0{,}1b)$$
15. $$a^4-b^2=(a^2-b)(a^2+b)$$
16. $$p^2t^2-0{,}36k^2d^2=(pt-0{,}6kd)(pt+0{,}6kd)$$
17. $$y^{10}-9=(y^5-3)(y^5+3)$$
18. $$4x^{12}-1\frac{11}{25}y^{16}=4x^{12}-\frac{36}{25}y^{16}$$
    $$ =\left(2x^6-\frac65y^8\right)\left(2x^6+\frac65y^8\right) $$
    $$ =(2x^6-1{,}2y^8)(2x^6+1{,}2y^8) $$

Ответ

1) $(b-d)(b+d)$; 2) $(x-1)(x+1)$; 3) $(1-x)(1+x)$; 4) $(6-c)(6+c)$; 5) $(2-5a)(2+5a)$; 6) $(7a-10)(7a+10)$; 7) $(30-9k)(30+9k)$; 8) $(4x-11y)(4x+11y)$; 9) $(bc-1)(bc+1)$; 10) $\left(\frac12x-\frac13y\right)\left(\frac12x+\frac13y\right)$; 11) $(5-2ab)(5+2ab)$; 12) $(12xy-20)(12xy+20)$; 13) $(abc-1)(abc+1)$; 14) $(10a-0{,}1b)(10a+0{,}1b)$; 15) $(a^2-b)(a^2+b)$; 16) $(pt-0{,}6kd)(pt+0{,}6kd)$; 17) $(y^5-3)(y^5+3)$; 18) $\left(2x^6-\frac65y^8\right)\left(2x^6+\frac65y^8\right)$.