Вариант 2
1. 15m²n - 5n²m = 5mn (3m - n)
2. 20a³ - 6b² - 24ab + 5a²b = 5a²(4a + b) - 6b(4a + b) = (5a² - 6b)(4a+b)
3. 2x² - 4xy² + 3xy - 6y³ = 2x ( x - 2y²) + 3y( x - 2y²) = (2x + 3y)(x - 2y²)
при x =
; y = 
( 2 * + 3*) ( - 2*
) = ( 
+ )( - 
) = 1*( 
- ) = 
4. a) 16x⁴ - 0,09a² = (4x² - 0,3a)(4x² + 0,3a)
б) 4a⁶b² - 20a³bc² + 25c⁴ = (2a³b - 5c²)²
в)
a² + ab + 
b² = (a + 
b)²
5. (x - 2y)³ + (x + 2y)³ = x³ - 6x²y + 6xy² - 8y³ + x³ + 6x²y + 6xy² - 8y³ = 2x³ + 12xy² - 16y³ = 2(x³ + 6xy² - 8y³)
6. 128² - 78² = (128 - 78)(128 + 78) = 50*206 = 10 300
7. 108³ - 7³ = (108 - 7)(108² + 108*7 + 7²) = 101(108² + 108*7 + 7²) - кратно 101
8.a) a³ + b³ (a + b)(a² - ab + b²) a² - ab + b²
---------- = ------------------------------ = ----------------
b² - a² (b - a)(b+a) b - a
б) 3a³b² - 18a²b³ + 27ab⁴ 3ab²(a² - 6b + 9b²) b(a - 3b)² b(a - 3b)
------------------------------- = ----------------------------- = ---------------- = -------------
6a³b - 18a²b² 6a²b(a - 3b) 2a(a - 3b) 2a
9.
1. 15m²n - 5n²m = 5mn (3m - n)
2. 20a³ - 6b² - 24ab + 5a²b = 5a²(4a + b) - 6b(4a + b) = (5a² - 6b)(4a+b)
3. 2x² - 4xy² + 3xy - 6y³ = 2x ( x - 2y²) + 3y( x - 2y²) = (2x + 3y)(x - 2y²)
при x =
( 2 *
4. a) 16x⁴ - 0,09a² = (4x² - 0,3a)(4x² + 0,3a)
б) 4a⁶b² - 20a³bc² + 25c⁴ = (2a³b - 5c²)²
в)
5. (x - 2y)³ + (x + 2y)³ = x³ - 6x²y + 6xy² - 8y³ + x³ + 6x²y + 6xy² - 8y³ = 2x³ + 12xy² - 16y³ = 2(x³ + 6xy² - 8y³)
6. 128² - 78² = (128 - 78)(128 + 78) = 50*206 = 10 300
7. 108³ - 7³ = (108 - 7)(108² + 108*7 + 7²) = 101(108² + 108*7 + 7²) - кратно 101
8.a) a³ + b³ (a + b)(a² - ab + b²) a² - ab + b²
---------- = ------------------------------ = ----------------
b² - a² (b - a)(b+a) b - a
б) 3a³b² - 18a²b³ + 27ab⁴ 3ab²(a² - 6b + 9b²) b(a - 3b)² b(a - 3b)
------------------------------- = ----------------------------- = ---------------- = -------------
6a³b - 18a²b² 6a²b(a - 3b) 2a(a - 3b) 2a
9.