Question

Упростите выражения: (a-2)^2, (a-3)(a+3), (x-1)(x^2+x+1), 2(c-2)(2+c), (x^2+3), (a-3)(a+6)

Answer 1

(a-2)²=a²-4a+4
(a-3)(a+3)=a²-9
(x-1)(x²+x+1)=(x-1)³
2(c-2)(2+c)=2(x²-4)=2x²-8
x²+3 - так и остаётся
(a-3)(a+6)=a²+3a-18

Answer 2

1) (a-2)^2: (a-2)^2 = (a-2)(a-2) = a^2 - 2a - 2a + 4 = a^2 - 4a + 4

2) (a-3)(a+3): (a-3)(a+3) = a(a+3) - 3(a+3) = a^2 + 3a - 3a - 9 = a^2 - 9

3) (x-1)(x^2+x+1): (x-1)(x^2+x+1) = x(x^2+x+1) - 1(x^2+x+1) = x^3 + x^2 + x - x^2 - x - 1 = x^3 - 1

4) 2(c-2)(2+c): 2(c-2)(2+c) = 2(c^2 - 2c + 2c - 4) = 2(c^2 - 4)

5) (x^2+3): The expression (x^2+3) is already simplified and cannot be further simplified.

6) (a-3)(a+6): (a-3)(a+6) = a(a+6) - 3(a+6) = a^2 + 6a - 3a - 18 = a^2 + 3a - 18