Упр.354 ГДЗ Колягин Ткачёва 7 класс (Алгебра)

1) (0,25)^7•4^7;
2) (4/5)^17•(5/4)^17;
3) (-0,125)^11•8^11;
4) (-0,2)^5•5^5.
Разложить на множители:
1) 36x^2 y^2-1;
2) 81a^6-49b^4;
3) x^2 y^4-16;
4) 25a^2-9b^6.

1. $$\left(0{,}25\right)^7 \cdot 4^7 = \left(0{,}25 \cdot 4\right)^7 = 1^7 = 1.$$
2. $$\left(\frac45\right)^{17} \cdot \left(\frac54\right)^{17} = \left(\frac45 \cdot \frac54\right)^{17} = 1^{17} = 1.$$
3. $$\left(-0{,}125\right)^{11} \cdot 8^{11} = \left(-0{,}125 \cdot 8\right)^{11} = (-1)^{11} = -1.$$
4. $$\left(-0{,}2\right)^5 \cdot 5^5 = \left(-0{,}2 \cdot 5\right)^5 = (-1)^5 = -1.$$

5. $$36x^2y^2 — 1 = (6xy)^2 — 1^2 = (6xy — 1)(6xy + 1).$$
6. $$81a^6 — 49b^4 = (9a^3)^2 — (7b^2)^2 = (9a^3 — 7b^2)(9a^3 + 7b^2).$$
7. $$x^2y^4 — 16 = (xy^2)^2 — 4^2 = (xy^2 — 4)(xy^2 + 4).$$
8. $$25a^2 — 9b^6 = (5a)^2 — (3b^3)^2 = (5a — 3b^3)(5a + 3b^3).$$

Ответ

1) $$1$$; 2) $$1$$; 3) $$-1$$; 4) $$-1$$.
1) $$\left(6xy — 1\right)\left(6xy + 1\right)$$;
2) $$\left(9a^3 — 7b^2\right)\left(9a^3 + 7b^2\right)$$;
3) $$\left(xy^2 — 4\right)\left(xy^2 + 4\right)$$;
4) $$\left(5a — 3b^3\right)\left(5a + 3b^3\right)$$.