~1. Упростиште a)(x-3)(x-7)-2x(3x-5) 5) 4a (a-2)-(a-4)² b) 2(m+1)²-4m a) x³-9x ; б)-5a²-10ab-5b² (y²=2y)²=y²(y+3)(y-3)+2y(2y²+5) od 16x⁴-81; S/x²x-y²=-y

Задание 1

a) \[ (x-3)(x-7)-2x(3x-5) = x^2 -7x -3x + 21 -6x^2 + 10x = -5x^2 -10x + 21 \]

б) \[ 4a(a-2)-(a-4)^2 = 4a^2 - 8a - (a^2 - 8a + 16) = 4a^2 - 8a - a^2 + 8a - 16 = 3a^2 - 16 \]

в) \[ 2(m+1)^2 - 4m = 2(m^2 + 2m + 1) - 4m = 2m^2 + 4m + 2 - 4m = 2m^2 + 2 \]

Задание 2

a) \[ x^3 - 9x = x(x^2 - 9) = x(x-3)(x+3) \]

б) \[ -5a^2 - 10ab - 5b^2 = -5(a^2 + 2ab + b^2) = -5(a+b)^2 \]

Задание 3

\[ (y^2 - 2y)^2 - y^2(y+3)(y-3) + 2y(2y^2+5) = \] \[ = y^4 - 4y^3 + 4y^2 - y^2(y^2 - 9) + 4y^3 + 10y = \] \[ = y^4 - 4y^3 + 4y^2 - y^4 + 9y^2 + 4y^3 + 10y = 13y^2 + 10y \]

Задание 4

a) \[ 16x^4 - 81 = (4x^2 - 9)(4x^2 + 9) = (2x-3)(2x+3)(4x^2+9) \]

б) \[ x^2 - x - y^2 - y = x^2 - y^2 - (x + y) = (x-y)(x+y) - (x+y) = (x+y)(x-y-1) \]

Ответ: Решения выше