Выполни действия и упрости выражения из контрольной работы.

Вариант 2 1. а) $15y^2 + 7y - (13y - 5y^2) = 15y^2 + 7y - 13y + 5y^2 = (15y^2 + 5y^2) + (7y - 13y) = 20y^2 - 6y$ б) $2c(a - 3b + 4) = 2c \cdot a - 2c \cdot 3b + 2c \cdot 4 = 2ac - 6bc + 8c$ в) $(4x - 1)(2x - 3) = 4x \cdot 2x - 4x \cdot 3 - 1 \cdot 2x + 1 \cdot 3 = 8x^2 - 12x - 2x + 3 = 8x^2 - 14x + 3$ г) $(a + 2)(a^2 - a - 3) = a \cdot a^2 - a \cdot a - a \cdot 3 + 2 \cdot a^2 - 2 \cdot a - 2 \cdot 3 = a^3 - a^2 - 3a + 2a^2 - 2a - 6 = a^3 + (-a^2 + 2a^2) + (-3a - 2a) - 6 = a^3 + a^2 - 5a - 6$ д) $(4ab^2 - 6a^2b) : 2ab = (4ab^2 : 2ab) - (6a^2b : 2ab) = 2b - 3a$ 2. $2x(3x - 4) - 3x(3x - 1) = 2x \cdot 3x - 2x \cdot 4 - 3x \cdot 3x + 3x \cdot 1 = 6x^2 - 8x - 9x^2 + 3x = (6x^2 - 9x^2) + (-8x + 3x) = -3x^2 - 5x$ 3. $1,5x(3x^2 - 5)(2x^2 + 3) = (1,5x \cdot 3x^2 - 1,5x \cdot 5)(2x^2 + 3) = (4,5x^3 - 7,5x)(2x^2 + 3) = 4,5x^3 \cdot 2x^2 + 4,5x^3 \cdot 3 - 7,5x \cdot 2x^2 - 7,5x \cdot 3 = 9x^5 + 13,5x^3 - 15x^3 - 22,5x = 9x^5 + (13,5x^3 - 15x^3) - 22,5x = 9x^5 - 1,5x^3 - 22,5x$ 4. $5a(a + b + c) - 5b(a - b - c) - 5c(a + b - c) = 5a \cdot a + 5a \cdot b + 5a \cdot c - 5b \cdot a + 5b \cdot b + 5b \cdot c - 5c \cdot a - 5c \cdot b + 5c \cdot c = 5a^2 + 5ab + 5ac - 5ab + 5b^2 + 5bc - 5ac - 5bc + 5c^2 = 5a^2 + 5b^2 + 5c^2 + (5ab - 5ab) + (5ac - 5ac) + (5bc - 5bc) = 5a^2 + 5b^2 + 5c^2$ Вариант 1 1. а) $2x^2 - xy = x(2x - y)$ б) $ab + 3ab^2 = ab(1 + 3b)$ г) $2a(a - 1) + 3(a - 1) = (a - 1)(2a + 3)$ д) $4x - 4y + ax - ay = 4(x - y) + a(x - y) = (x - y)(4 + a)$