885. Выполните умножение:

Решение:

Применим формулы сокращённого умножения:

1. \( (b-2)(b+2)(b^2+4) = (b^2-4)(b^2+4) = b^4-16 \)

2. \( (3-y)(3+y)(9+y^2) = (9-y^2)(9+y^2) = 81-y^4 \)

3. \( (a^2+1)(a+1)(a-1) = (a^2+1)(a^2-1) = a^4-1 \)

4. \( (c^4+1)(c^2+1)(c^2-1) = (c^4+1)(c^4-1) = c^8-1 \)

5. \( (x-3)^2(x+3)^2 = ((x-3)(x+3))^2 = (x^2-9)^2 = x^4-18x^2+81 \)

6. \( (y+4)^2(y-4)^2 = ((y+4)(y-4))^2 = (y^2-16)^2 = y^4-32y^2+256 \)

7. \( (a-5)^2(5+a)^2 = ((a-5)(a+5))^2 = (a^2-25)^2 = a^4-50a^2+625 \)

8. \( (c+4)^2(4-c)^2 = ((4+c)(4-c))^2 = (16-c^2)^2 = 256-32c^2+c^4 \)

Ответ:

a) \( b^4-16 \)

б) \( 81-y^4 \)

в) \( a^4-1 \)

г) \( c^8-1 \)

д) \( x^4-18x^2+81 \)

е) \( y^4-32y^2+256 \)

ж) \( a^4-50a^2+625 \)

з) \( c^4-32c^2+256 \)