1) 62-49; 2) c²-8c+16; 3) 100-9x2; 5/3x-3y+xy-xy² 4) 4a² +20ab+2562 6193-8 3.° Упростите выражение (х-2)(x+2)-(x-5)². 4.° Решите уравнение: a) (x-1)(x + 1) – x(x - 2) = 0; 6) x²-4 = 0.

Задание 1

1. \[b^2 - 49 = (b-7)(b+7)\]

2. \[c^2 - 8c + 16 = (c-4)^2\]

3. \[100 - 9x^2 = (10-3x)(10+3x)\]

4. \[4a^2 + 20ab + 25b^2 = (2a+5b)^2\]

5. \[3x-3y+x^2y-xy^2 = 3(x-y) + xy(x-y) = (x-y)(3+xy)\]

6. \[a^3 - 8 = (a-2)(a^2+2a+4)\]

Задание 3

\[(x-2)(x+2)-(x-5)^2 = x^2-4-(x^2-10x+25) = x^2-4-x^2+10x-25 = 10x - 29\]

Задание 4

a) \[(x-1)(x+1) - x(x-2) = 0\]

\[x^2 - 1 - x^2 + 2x = 0\]

\[2x = 1\]

\[x = \frac{1}{2}\]

б) \[x^2 - 4 = 0\]

\[x^2 = 4\]

\[x = \pm 2\]