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Представьте в виде произведения многочлен:
1) $x^2-36$;
2) $1-a^2$;
3) $16-x^2$;
4) $-y^2 +81$;
5) $\frac{1}{9}-b^2$;
6) $y^2 - \frac{25}{36}$;
7) $0,81-x^2$;
8) $16a^2-1$;
9) $100-9y^2$;
10) $36a^2-25b^2$;
11) $-9p^2 +0,16q^2$;
12) $\frac{4}{81}k^2-\frac{1}{25}b^2$;
13) $7\frac{1}{9}n^2-4m^2$;
14) $0,04x^2 -0,64y^2$;
15) $9m^2n^2-1$;
16) $81-16p^2q^2$;
17) $0,01a^2b^2-100m^2$;
18) $121a^2b^4-49c^2$;
19) $9x^4z^2-0,09y^2$;
20) $-\frac{9}{64}t^2 +36k^4l^6$
Вопрос:
Представьте в виде произведения многочлен:
1) $$x^2-36$$;
2) $$1-a^2$$;
3) $$16-x^2$$;
4) $$-y^2 +81$$;
5) $$\frac{1}{9}-b^2$$;
6) $$y^2 - \frac{25}{36}$$;
7) $$0,81-x^2$$;
8) $$16a^2-1$$;
9) $$100-9y^2$$;
10) $$36a^2-25b^2$$;
11) $$-9p^2 +0,16q^2$$;
12) $$\frac{4}{81}k^2-\frac{1}{25}b^2$$;
13) $$7\frac{1}{9}n^2-4m^2$$;
14) $$0,04x^2 -0,64y^2$$;
15) $$9m^2n^2-1$$;
16) $$81-16p^2q^2$$;
17) $$0,01a^2b^2-100m^2$$;
18) $$121a^2b^4-49c^2$$;
19) $$9x^4z^2-0,09y^2$$;
20) $$-\frac{9}{64}t^2 +36k^4l^6$$
Ответ:
Решение заданий
- $$x^2 - 36 = (x - 6)(x + 6)$$
- $$1 - a^2 = (1 - a)(1 + a)$$
- $$16 - x^2 = (4 - x)(4 + x)$$
- $$-y^2 + 81 = 81 - y^2 = (9 - y)(9 + y)$$
- $$\frac{1}{9} - b^2 = (\frac{1}{3} - b)(\frac{1}{3} + b)$$
- $$y^2 - \frac{25}{36} = (y - \frac{5}{6})(y + \frac{5}{6})$$
- $$0.81 - x^2 = (0.9 - x)(0.9 + x)$$
- $$16a^2 - 1 = (4a - 1)(4a + 1)$$
- $$100 - 9y^2 = (10 - 3y)(10 + 3y)$$
- $$36a^2 - 25b^2 = (6a - 5b)(6a + 5b)$$
- $$-9p^2 + 0.16q^2 = 0.16q^2 - 9p^2 = (0.4q - 3p)(0.4q + 3p)$$
- $$\frac{4}{81}k^2 - \frac{1}{25}b^2 = (\frac{2}{9}k - \frac{1}{5}b)(\frac{2}{9}k + \frac{1}{5}b)$$
- $$7\frac{1}{9}n^2 - 4m^2 = (\frac{8}{3}n - 2m)(\frac{8}{3}n + 2m)$$
- $$0.04x^2 - 0.64y^2 = (0.2x - 0.8y)(0.2x + 0.8y)$$
- $$9m^2n^2 - 1 = (3mn - 1)(3mn + 1)$$
- $$81 - 16p^2q^2 = (9 - 4pq)(9 + 4pq)$$
- $$0.01a^2b^2 - 100m^2 = (0.1ab - 10m)(0.1ab + 10m)$$
- $$121a^2b^4 - 49c^2 = (11ab^2 - 7c)(11ab^2 + 7c)$$
- $$9x^4z^2 - 0.09y^2 = (3x^2z - 0.3y)(3x^2z + 0.3y)$$
- $$-\frac{9}{64}t^2 + 36k^4l^6 = 36k^4l^6 - \frac{9}{64}t^2 = (6k^2l^3 - \frac{3}{8}t)(6k^2l^3 + \frac{3}{8}t)$$
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