2. Преобразуйте в многочлен: 1) а) (a−4) (a +4)-2a (3-a); 2) а) (a-8) (a- 7) – (a – 9)²; 3) а) (b+3)(b-3)+(2b+3)²; 4) а) 3(x-5)² + (10x-8x²); б) (4х-3)²-6x (4-x); б) (p+3)(p-11)+(p+6)²; б) (а-х)²+(a+x)²; б) 2(x+6)²-(20x+70).

Краткое пояснение:

Пошаговое решение:

• 1. а)
  \[ (a-4)(a+4) - 2a(3-a) = (a^2 - 16) - (6a - 2a^2) = a^2 - 16 - 6a + 2a^2 = 3a^2 - 6a - 16 \]
• 1. б)
  \[ (4x-3)^2 - 6x(4-x) = (16x^2 - 24x + 9) - (24x - 6x^2) = 16x^2 - 24x + 9 - 24x + 6x^2 = 22x^2 - 48x + 9 \]
• 2. а)
  \[ (a-8)(a-7) - (a-9)^2 = (a^2 - 7a - 8a + 56) - (a^2 - 18a + 81) = a^2 - 15a + 56 - a^2 + 18a - 81 = 3a - 25 \]
• 2. б)
  \[ (p+3)(p-11) + (p+6)^2 = (p^2 - 11p + 3p - 33) + (p^2 + 12p + 36) = p^2 - 8p - 33 + p^2 + 12p + 36 = 2p^2 + 4p + 3 \]
• 3. а)
  \[ (b+3)(b-3) + (2b+3)^2 = (b^2 - 9) + (4b^2 + 12b + 9) = b^2 - 9 + 4b^2 + 12b + 9 = 5b^2 + 12b \]
• 3. б)
  \[ (a-x)^2 + (a+x)^2 = (a^2 - 2ax + x^2) + (a^2 + 2ax + x^2) = a^2 - 2ax + x^2 + a^2 + 2ax + x^2 = 2a^2 + 2x^2 \]
• 4. а)
  \[ 3(x-5)^2 + (10x-8x^2) = 3(x^2 - 10x + 25) + 10x - 8x^2 = 3x^2 - 30x + 75 + 10x - 8x^2 = -5x^2 - 20x + 75 \]
• 4. б)
  \[ 2(x+6)^2 - (20x+70) = 2(x^2 + 12x + 36) - 20x - 70 = 2x^2 + 24x + 72 - 20x - 70 = 2x^2 + 4x + 2 \]