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1) x² - 2x - 48 = 0;

D = b² - 4ac;

D = (-2)²- 4 • 1 • (-48) = 4 + 192 = 196; √D = 14;

x = (-b ± √D)/(2a);

x1 = (2 + 14)/2 = 16/2 = 8;

x2 = (2 - 14)/2 = - 12/2 = -6;

x² - 2x - 48 (x - 8)(x + 6).

2) 2x²- 5x + 3 = 0;

D = (-5)² - 4 • 2 • 3 = 25 + 24 = 49; √D = 7;

x1 = (5 + 7)/4 = 12/4 = 3;

x2 = (5 - 7)/4 = -2/4 = -0,5;

2x² - 5x + 3 = 2(x + 0,5)(x - 3) = (2x + 1)(x - 3).

3) 3x² - 10x + 3 = 0;

D = (-10)² - 4 • 3 • 3 = 100 - 36 = 64; √D = 8;

x1 = (10 + 8)/6 = 18/6 = 3;

x2 = (10 - 8)/6 = 2/6 = 1/3;

3x² - 10x + 3 = 3(x - 1/3)(x - 3) = (3x - 1)(x - 3).

4) 5x² - x - 42 = 0;

D = (-1)^2 - 4 • 5 • (-42) = 1 + 840 = 841; √D = 29;

x1 = (1 + 29)/10 = 30/10 = 3;

x2 = (1 - 29)/10 = -28/10 = -2,8;

5x² - x - 42 = 5(x + 2,8)(x - 3) = (5x +14)(x - 3).

5) 3x² - 8x + 5 = 0;

D = (-8)^2 - 4 • 3 • 5 = 64 - 60 = 4; √D = 2;

x1 = (8 + 2)/6 = 10/6 = 5/3;

x2 = (8 - 2)/6 = 6/6 = 1;

3x² -8x + 5 = 3(x - 5/3)(x - 1) = (3x - 5)(x - 1).

6) 36x² - 12x + 1 = 0;

D = (-12)^2 - 4 • 36 • 1 = 144 - 144 = 0;

x1 = x2 = 12/72 = 1/6;

36x²- 12x + 1 = 36(x - 1/6)(x - 1/6) = 6(x - 1/6) * 6(x - 1/6) = (6x - 1)(6x - 1).

1.
1) x²+(5x-3)²=x²+25x²-30x+9=26x²-30x+9
2) (p-2c)²+3p²=p²-4pc+4c²+3p²=4p²-4pc+4c²
3) (3a-7b)²-42ab=9a²-42ab+49b²-42ab=9a²-84ab+49b²
4) 81x²-(9x+7y)²=81x²-(81x²+126xy+49y²)=81x²-81x²-126xy-49y²=-126xy-49y²
2.
1) (2x-3y)²+(3x+2y)²=4x²-12xy+9y²+9x²+12xy+4y²=13x²+13y²
2) (5а+3b)²-(5а-3b)²=25a²+30ab+9b²-25a²+30ab-9b²=60ab
3) a-b)²+2ab)²-2a²b²)²-2a⁴b⁴)²-a¹⁶-b¹⁶ Разложим на действия
 Действие ₁= ((a-b)²+2ab)²=(a²-2ab+b²+2ab)²=(a²+b²)²=a⁴+2a²b²+b⁴
Действие ₂=(a⁴+2a²b²+b⁴-2a²b²)²=(a⁴+b⁴)²=a⁸+2a⁴b⁴+b⁸
Действие ₃= (b⁸+2a⁴b⁴+a⁸-2a⁴b⁴)²=(a⁸+b⁸)² =a¹⁶+2a⁸b⁸+b¹⁶
Действие ₄=  a¹⁶+2a⁸b⁸+b¹⁶ - a¹⁶- b¹⁶ = 2a⁸b⁸
ответ 2a⁸b⁸