Разложите многочлен на множители N1. 1) a) ax-ay+bx-by; б) 5а+5у+pa+py; 2) a) 2x+ac+cx+2a; 6) 2x+7y+14+xy; 3) a) ab+ac-4b-4c; б) За-3m-ay+my. N2. 1) a) 2ax+3by+6ay+bx; в) ау-12bx+3ax-4by; б) 3с+3с²-а-ас; г) a²b²+ab+abc+c; 2) a) ax+bx+cx+ay+by+cy;

Ответ: смотри решение ниже

N1

1) a)

\[ax - ay + bx - by = a(x - y) + b(x - y) = (a + b)(x - y)\]

1) б)

\[5a + 5y + pa + py = 5(a + y) + p(a + y) = (5 + p)(a + y)\]

2) a)

\[2x + ac + cx + 2a = 2(x + a) + c(x + a) = (2 + c)(x + a)\]

2) б)

\[2x + 7y + 14 + xy = 2x + xy + 7y + 14 = x(2 + y) + 7(y + 2) = (x + 7)(y + 2)\]

3) a)

\[ab + ac - 4b - 4c = a(b + c) - 4(b + c) = (a - 4)(b + c)\]

3) б)

\[3a - 3m - ay + my = 3(a - m) - y(a - m) = (3 - y)(a - m)\]

N2

1) a)

\[2ax + 3by + 6ay + bx = 2ax + bx + 6ay + 3by = x(2a + b) + 3y(2a + b) = (x + 3y)(2a + b)\]

1) в)

\[ay - 12bx + 3ax - 4by = ay - 4by + 3ax - 12bx = y(a - 4b) + 3x(a - 4b) = (y + 3x)(a - 4b)\]

1) б)

\[3c + 3c^2 - a - ac = 3c(1 + c) - a(1 + c) = (3c - a)(1 + c)\]

1) г)

\[a^2b^2 + ab + abc + c = ab(ab + 1) + c(ab + 1) = (ab + c)(ab + 1)\]

2) a)

\[ax + bx + cx + ay + by + cy = x(a + b + c) + y(a + b + c) = (x + y)(a + b + c)\]

Ответ: смотри решение выше