128. Упростите выражение.

Решение:

1. \( (x-5)^2 - 7 = x^2 - 10x + 25 - 7 = x^2 - 10x + 18 \)
2. \( 6y + (y-3)^2 = 6y + y^2 - 6y + 9 = y^2 + 9 \)
3. \( (4a-5b)^2 - 16a(a-3b) = 16a^2 - 40ab + 25b^2 - 16a^2 + 48ab = 8ab + 25b^2 \)
4. \( (4m+3n)^2 + (2m-6n)^2 = (16m^2 + 24mn + 9n^2) + (4m^2 - 24mn + 36n^2) = 20m^2 + 45n^2 \)
5. \( x(x-2) - (x-3)^2 = x^2 - 2x - (x^2 - 6x + 9) = x^2 - 2x - x^2 + 6x - 9 = 4x - 9 \)
6. \( (8p-q)^2 - (4p-q)(16p+3q) = (64p^2 - 16pq + q^2) - (64p^2 + 12pq - 16pq - 3q^2) = 64p^2 - 16pq + q^2 - (64p^2 - 4pq - 3q^2) = 64p^2 - 16pq + q^2 - 64p^2 + 4pq + 3q^2 = -12pq + 4q^2 \)
7. \( y(3y-2)^2 - 9y(4+y)^2 = y(9y^2 - 12y + 4) - 9y(16 + 8y + y^2) = 9y^3 - 12y^2 + 4y - 9y(16 + 8y + y^2) = 9y^3 - 12y^2 + 4y - 144y - 72y^2 - 9y^3 = -84y^2 - 140y \)
8. \( (x+4)^2 - (x-2)(x+2) = x^2 + 8x + 16 - (x^2 - 4) = x^2 + 8x + 16 - x^2 + 4 = 8x + 20 \)
9. \( (8a-3b)(8a+3b) - (6a-5b)^2 = (64a^2 - 9b^2) - (36a^2 - 60ab + 25b^2) = 64a^2 - 9b^2 - 36a^2 + 60ab - 25b^2 = 28a^2 + 60ab - 34b^2 \)
10. \( (m-3)(m+4) - (m+2)^2 + (4-m)(m+4) = (m^2 + 4m - 3m - 12) - (m^2 + 4m + 4) + (4m + 16 - m^2 - 4m) = (m^2 + m - 12) - (m^2 + 4m + 4) + (16 - m^2) = m^2 + m - 12 - m^2 - 4m - 4 + 16 - m^2 = -m^2 - 3m \)

Ответ: 1) \( x^2 - 10x + 18 \); 2) \( y^2 + 9 \); 3) \( 8ab + 25b^2 \); 4) \( 20m^2 + 45n^2 \); 5) \( 4x - 9 \); 6) \( -12pq + 4q^2 \); 7) \( -84y^2 - 140y \); 8) \( 8x + 20 \); 9) \( 28a^2 + 60ab - 34b^2 \); 10) \( -m^2 - 3m \).