Представьте целое выражение в виде произведения многочленов:
а) 86x − 43y + 2ax − ay;
б) 10by − 25bx − 6ay + 15ax;
в) $x^2 + xy - xz - yz$;
г) $m^4 + 2 - m - 2m^3$;
д) $5a^2 - 5ab + 5b^2 - 5ab$;
е) $y - y^2 - y^3 + y^4$;
ж) $b^3 + b^2c - b^2d - bcd$;
з) $x^2y - z^2x + y^2x - yz^2$.
86x − 43y + 2ax − ay = (86x − 43y) + (2ax − ay) = 43(2x − y) + a(2x − y) = (2x − y)(43 + a)
10by − 25bx − 6ay + 15ax = (10by − 25bx) − (6ay − 15ax) = 5b(2y − 5x) − 3a(2y − 5x) = (2y − 5x)(5b − 3a)
$x^2 + xy - xz - yz = (x^2 + xy) - (xz + yz) = x(x + y) - z(x + y) = (x + y)(x - z)$
$m^4 + 2 - m - 2m^3 = (m^4 - 2m^3) + (2 - m) = m^3(m - 2) - (m - 2) = (m - 2)(m^3 - 1) = (m - 2)(m - 1)(m^2 + m + 1)$
$5a^2 - 5ab + 5b^2 - 5ab = (5a^2 - 5ab) + (5b^2 - 5ab) = 5a(a - b) + 5b(b - a) = 5a(a - b) - 5b(a - b) = (a - b)(5a - 5b) = 5(a - b)(a - b) = 5(a - b)^2$
$y - y^2 - y^3 + y^4 = (y - y^2) - (y^3 - y^4) = y(1 - y) - y^3(1 - y) = (1 - y)(y - y^3) = y(1 - y)(1 - y^2) = y(1 - y)(1 - y)(1 + y) = y(1 - y)^2(1 + y)$
$b^3 + b^2c - b^2d - bcd = (b^3 + b^2c) - (b^2d + bcd) = b^2(b + c) - bd(b + c) = (b + c)(b^2 - bd) = b(b + c)(b - d)$
$x^2y - z^2x + y^2x - yz^2 = (x^2y + y^2x) - (z^2x + yz^2) = xy(x + y) - z^2(x + y) = (x + y)(xy - z^2)$
Пожауйста, оцените решение
