1.
а) a² * 24b³ = 4a
6b³ a
б) 21x³y : 7x³y² = 21x³y * 3 = 9
3 7x³y² y
в) m-3n * m² - n² = m-3n * (m-n)(m+n) = m-n
m+n 3m-9n m+n 3(m-3n) 3
г) x² -16 : x² -4x = (x-4)(x+4) * x+2 = x+4 = x+4
x²+4x+4 x+2 (x+2)² x(x-4) x(x+2) x²+2x
3.
a) ( 9y - 9y ) * (x+y)² = ( 9y(x+y)-9xy ) * (x+y)² =
x x+y 3y x(x+y) 3y
= 9xy+9y²-9xy * x+y = 9y² * x+y = 3y(x+y) = 3xy+3y²
x 3y x 3y x x
б) (4x - 12x ) : ( х - 8х -25 ) = (4х(х-2)-12х) : (х(х-2)-(8х-25)) =
х-2 х-2 х-2 х-2
= 4x²-8x-12x * x-2 = 4x² -20x = 4x(x-5) = 4x
x-2 x²-2x-8x+25 x²-10x+25 (x-5)² x-5