Вариант 1 1. ax + ay + bx + by 2. 2am-3an+4bm-6bn 3. x²+2xy+xz+ 2yz 4. ab-2b+a2-2a 5. xy-5y+2x-10 6. 6ac3bc8ad-4bd 7. m³ + m² + m+ 1 8. a²ba²c + ab² - abc 9. 2x3-6x2+x-3 10. x²y + 3x²-2y-6 11. 3a26ab + 5a - 10b 12. 4xy-6y2-10x + 15y Вариант 2 1. mx+my+nx + ny 2. 3ap+4aq6bp-8bq 3. y2-3yz+xy-3xz 4. pq + 5q + p2 + 5p 5. mn+3n-4m-12 6. 10ad5bd+6ac - 3bc 7. n3n2n-1 8. c2d+c2e-cd2 - cde 9. 5y3+10y2+y+2 10. ab2+2b2-3a-6 11. 2x²+4xy-3x-6y 12. 6pq-9q2+8p-124

Привет! Это задания по алгебре, сейчас мы их разберем. Вариант 1 1. ax + ay + bx + by = a(x+y) + b(x+y) = (a+b)(x+y) 2. 2am - 3an + 4bm - 6bn = 2a(m - \frac{3}{2}n) + 4b(m - \frac{3}{2}n) = (2a + 4b)(m - \frac{3}{2}n) 3. x² + 2xy + xz + 2yz = x(x + 2y + z) + 2yz 4. ab - 2b + a² - 2a = b(a - 2) + a(a - 2) = (a + b)(a - 2) 5. xy - 5y + 2x - 10 = y(x - 5) + 2(x - 5) = (y + 2)(x - 5) 6. 6ac - 3bc + 8ad - 4bd = 3c(2a - b) + 4d(2a - b) = (3c + 4d)(2a - b) 7. m³ + m² + m + 1 = m²(m + 1) + 1(m + 1) = (m² + 1)(m + 1) 8. a²b - a²c + ab² - abc = a²(b - c) + ab(b - c) = (a² + ab)(b - c) = a(a + b)(b - c) 9. 2x³ - 6x² + x - 3 = 2x²(x - 3) + 1(x - 3) = (2x² + 1)(x - 3) 10. x²y + 3x² - 2y - 6 = x²(y + 3) - 2(y + 3) = (x² - 2)(y + 3) 11. 3a² - 6ab + 5a - 10b = 3a(a - 2b) + 5(a - 2b) = (3a + 5)(a - 2b) 12. 4xy - 6y² - 10x + 15y = 2y(2x - 3y) - 5(2x - 3y) = (2y - 5)(2x - 3y) Вариант 2 1. mx + my + nx + ny = m(x + y) + n(x + y) = (m + n)(x + y) 2. 3ap + 4aq - 6bp - 8bq = a(3p + 4q) - 2b(3p + 4q) = (a - 2b)(3p + 4q) 3. y² - 3yz + xy - 3xz = y(y - 3z) + x(y - 3z) = (y + x)(y - 3z) 4. pq + 5q + p² + 5p = q(p + 5) + p(p + 5) = (q + p)(p + 5) 5. mn + 3n - 4m - 12 = n(m + 3) - 4(m + 3) = (n - 4)(m + 3) 6. 10ad - 5bd + 6ac - 3bc = 5d(2a - b) + 3c(2a - b) = (5d + 3c)(2a - b) 7. n³ - n² + n - 1 = n²(n - 1) + 1(n - 1) = (n² + 1)(n - 1) 8. c²d + c²e - cd² - cde = c²(d + e) - cd(d + e) = (c² - cd)(d + e) = c(c - d)(d + e) 9. 5y³ + 10y² + y + 2 = 5y²(y + 2) + 1(y + 2) = (5y² + 1)(y + 2) 10. ab² + 2b² - 3a - 6 = b²(a + 2) - 3(a + 2) = (b² - 3)(a + 2) 11. 2x² + 4xy - 3x - 6y = 2x(x + 2y) - 3(x + 2y) = (2x - 3)(x + 2y) 12. 6pq - 9q² + 8p - 12q = 3q(2p - 3q) + 4(2p - 3q) = (3q + 4)(2p - 3q)

Ответ: смотри выше.

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