Представьте в виде произведения многочлен:
1) 3ab + 15b − 3a − 15;
2) 84 − 42y − 7xy + 14x;
3) abc + 6ac + 8ab + 48a;
4) $m^3 - m^2n + m^2 - mn$;
5) $a^3 + a^2 - a - 1$;
6) $2x^3 - 2xy^2 - 8x^2 + 8y^2$;
7) $5a^2 - 5b^2 - 15a^3b + 15ab^3$;
8) $a^2b^2 - 1 - b^2 + a^2$.
3ab + 15b − 3a − 15 = (3ab + 15b) − (3a + 15) = 3b(a + 5) − 3(a + 5) = (a + 5)(3b − 3) = 3(a + 5)(b − 1)
84 − 42y − 7xy + 14x = (84 − 42y) − (7xy − 14x) = 42(2 − y) − 7x(y − 2) = (2 − y)(42 + 7x) = 7(2 − y)(6 + x)
abc + 6ac + 8ab + 48a = (abc + 6ac) + (8ab + 48a) = ac(b + 6) + 8a(b + 6) = (b + 6)(ac
+ 8a) = a(b + 6)(c + 8)
$m^3 - m^2n + m^2 - mn = (m^3 - m^2n) + (m^2 - mn) = m^2(m - n) + m(m - n) = (m - n)(m^2 + m) = m(m - n)(m + 1)$
$a^3 + a^2 - a - 1 = (a^3 + a^2) - (a + 1) = a^2(a + 1) - (a + 1) = (a + 1)(a^2 - 1) = (a + 1)(a - 1)(a + 1)$
$2x^3 - 2xy^2 - 8x^2 + 8y^2 = (2x^3 - 2xy^2) - (8x^2 - 8y^2) = 2x(x^2 - y^2) - 8(x^2 - y^2) = (x^2 - y^2)(2x - 8) = 2(x^2 - y^2)(x - 4) = 2(x - y)(x + y)(x - 4)$
$5a^2 - 5b^2 - 15a^3b + 15ab^3 = (5a^2 - 5b^2) - (15a^3b - 15ab^3) = 5(a^2 - b^2) - 15ab(a^2 - b^2) = (a^2 - b^2)(5 - 15ab) = 5(a^2 - b^2)(1 - 3ab) = 5(a - b)(a + b)(1 - 3ab)$
$a^2b^2 - 1 - b^2 + a^2 = (a^2b^2 + a^2) - (1 + b^2) = a^2(b^2 + 1) - (b^2 + 1) = (b^2 + 1)(a^2 - 1) = (b^2 + 1)(a - 1)(a + 1)$
Пожауйста, оцените решение
