1) (x+3) (x-7)-4x5-2x); 2) (y + 2) (y - 6) + (y + 3)(y- 4); 3) (a - 3) (3а + 1) - (2a + 3) (4а - 1); 4) (x+4)2-(x-2) (x+2); 5) (8a - 3b) (8a + 3b) - (6a - 5b) ; 6) (m - 3)(m+ 4) -…

Let's simplify each of the given expressions step by step.

1. Simplifying \( (x + 3)(x - 7) - 4x^5 - 2x \)

   Expanding \( (x + 3)(x - 7) \): \[ (x + 3)(x - 7) = x^2 - 7x + 3x - 21 = x^2 - 4x - 21 \]

   Now, substituting back: \[ x^2 - 4x - 21 - 4x^5 - 2x = -4x^5 + x^2 - 6x - 21 \]

   Thus, the simplified expression is: \[ -4x^5 + x^2 - 6x - 21 \]

2. Simplifying \( (y + 2)(y - 6) + (y + 3)(y - 4) \)

   Expanding both products: \[ (y + 2)(y - 6) = y^2 - 6y + 2y - 12 = y^2 - 4y - 12 \] \[ (y + 3)(y - 4) = y^2 - 4y + 3y - 12 = y^2 - y - 12 \]

   Now adding both results: \[ (y^2 - 4y - 12) + (y^2 - y - 12) = 2y^2 - 5y - 24 \]

   Thus, the simplified expression is: \[ 2y^2 - 5y - 24 \]

3. Simplifying \( (a - 3)(3a + 1) - (2a + 3)(4a - 1) \)

   Expanding both products: \[ (a - 3)(3a + 1) = 3a^2 + a - 9a - 3 = 3a^2 - 8a - 3 \]

   \[ (2a + 3)(4a - 1) = 8a^2 - 2a + 12a - 3 = 8a^2 + 10a - 3 \]

   Now substituting back: \[ (3a^2 - 8a - 3) - (8a^2 + 10a - 3) = 3a^2 - 8a - 3 - 8a^2 - 10a + 3 \]

   Combining like terms: \[ (3a^2 - 8a^2) + (-8a - 10a) + (-3 + 3) = -5a^2 - 18a \]

   Thus, the simplified expression is: \[ -5a^2 - 18a \]

4. Simplifying \( (x + 4)^2 - (x - 2)(x + 2) \)

   Expanding \( (x + 4)^2 \): \[ (x + 4)^2 = x^2 + 8x + 16 \]

   Expanding \( (x - 2)(x + 2) \) using the difference of squares: \[ (x - 2)(x + 2) = x^2 - 4 \]

   Now substituting back: \[ x^2 + 8x + 16 - (x^2 - 4) = x^2 + 8x + 16 - x^2 + 4 \]

   Combining like terms: \[ 8x + 20 \]

   Thus, the simplified expression is: \[ 8x + 20 \]

5. Simplifying \( (8a - 3b)(8a + 3b) - (6a - 5b) \)

   Expanding \( (8a - 3b)(8a + 3b) \) using the difference of squares: \[ (8a)^2 - (3b)^2 = 64a^2 - 9b^2 \]

   Now substituting back: \[ 64a^2 - 9b^2 - (6a - 5b) = 64a^2 - 9b^2 - 6a + 5b \]

   Thus, the simplified expression is: \[ 64a^2 - 6a - 9b^2 + 5b \]

6. Simplifying \( (m - 3)(m + 4) - (m + 2) + (4 - m)(m + 4) \)

   Expanding \( (m - 3)(m + 4) \): \[ m^2 + 4m - 3m - 12 = m^2 + m - 12 \]

   Expanding \( (4 - m)(m + 4) \): \[ 4m + 16 - m^2 - 4m = -m^2 + 16 \]

   Now substituting back: \[ (m^2 + m - 12) - (m + 2) + (-m^2 + 16) \] \[ = m^2 + m - 12 - m - 2 - m^2 + 16 \]

   Combining like terms: \[ 0m^2 + 0m + 2 = 2 \]

   Thus, the simplified expression is: \[ 2 \]

This completes the simplification of all given expressions.