1a) ay - 12bx + 3ax - 4by = (ay - 4by) + (3ax - 12bx) = y(a - 4b) + 3x(a - 4b) = (a - 4b)(y + 3x)
1б) x² - 8x + 15 = (x - 5)(x - 3)
2a) (y - 5)² - ( y - 2)5y = y² - 10y + 25 - 5y² + 10y = - 6y² + 25
2б) - 4(p - 2a)² = -4(p² - 4ap + 4a²) = - 4p² + 16ap - 16a²
3a) 16x² + 8xy + y² = (4x + y)²
3б) 49p² - 14p + 1 = (7p - 1)²
4a) (3 - 1/5a)(3 + 1/5a) = 3² - (1/5a)² = 9 - 1/25a² = 9 - 0,04a²
4б) (5b² + 1)(1 - 5b²) = 1² - (5b²)² = 1 - 5b⁴
5a) x²y⁴ - 1 = (xy²)² - 1² = (xy² - 1)(xy² + 1)
5б) 81 - 64x²y² = 9² - (8xy)² = (9 - 8xy)(9 + 8xy)
2a^2+2ab-2ac-2ba+2b^2+2bc+2ca-2cb+2c^2=2a^2+2b^2+2c^2.
sin2a=2sinacosa=-2*3*4/25=-24/25
sina=3/5 cosa=-4/5
tga/2=sina/(1-cosa)=sqrt(3)/2(1+1/2)=sqrt(3)/3
cosa=-1/2
= (2,5-2,3)(2,5+2,3) / (5,7-5,9)² = 0,2*4,8 / (-0,2)² = 4,8/0,2 = 48/2 = 24