Преобразуйте выражение в многочлен: a) a^2 + (3a - b)^2 = б) 9b^2 - (a - 3b)^2 = в) (5a + 7b)^2 - 70ab = г) (8a - b)^2 - 64a^2 = д) (5 + y)^2 + y(y - 7) = e) a(4 - a) + (4 - a)^2 = ж) (x - 8)^2 - 2x(6 - x)^2 =

Решение:

1. \( a^2 + (3a - b)^2 = a^2 + (9a^2 - 6ab + b^2) = a^2 + 9a^2 - 6ab + b^2 = 10a^2 - 6ab + b^2 \)
2. \( 9b^2 - (a - 3b)^2 = 9b^2 - (a^2 - 6ab + 9b^2) = 9b^2 - a^2 + 6ab - 9b^2 = -a^2 + 6ab \)
3. \( (5a + 7b)^2 - 70ab = (25a^2 + 70ab + 49b^2) - 70ab = 25a^2 + 49b^2 \)
4. \( (8a - b)^2 - 64a^2 = (64a^2 - 16ab + b^2) - 64a^2 = -16ab + b^2 \)
5. \( (5 + y)^2 + y(y - 7) = (25 + 10y + y^2) + (y^2 - 7y) = 25 + 10y + y^2 + y^2 - 7y = 2y^2 + 3y + 25 \)
6. \( a(4 - a) + (4 - a)^2 = 4a - a^2 + (16 - 8a + a^2) = 4a - a^2 + 16 - 8a + a^2 = -4a + 16 \)
7. \( (x - 8)^2 - 2x(6 - x)^2 = (x^2 - 16x + 64) - 2x(36 - 12x + x^2) = x^2 - 16x + 64 - 72x + 24x^2 - 2x^3 = -2x^3 + (x^2 + 24x^2) + (-16x - 72x) + 64 = -2x^3 + 25x^2 - 88x + 64 \)

Ответ: 10a² - 6ab + b²; -a² + 6ab; 25a² + 49b²; -16ab + b²; 2y² + 3y + 25; -4a + 16; -2x³ + 25x² - 88x + 64.