1.
1)
38² - 64 = 38² - 8² = (38 - 8)(38 +8) = 30 * 46 = 1380,
2.
1)
2в² - 18 = 2 * (в² - 9) = 2 * (в - 3)(в + 3),
3)
81х² - 18ху + у² + 63х - 7у = (81х² - 18ху + у²) + (63х - 7у) =
= (9х - у)² + 7*(9х - у) = (9х - у)(9х - у + 7),
4)
m² + n² + 2mn = (m + n)².
3.
а)
(8 - 2n)(8 + 2n) + (9 + 2n)² - 64 = 64 - 4n² + 81 + 36n + 4n² - 64 =
= 36n + 81 = 9(4n + 9),
б)
(3х - 8)² + (4х - 8)(4х + 8) = 9х² - 48х + 64 + 16х² - 64 = 25х² - 48х,
при х=-2:
25 * (-2)² - 48 * (-2) = 100 + 96 = 196,
4.
1 число - х,
2 число - (х+2),
(х+2)² - х² = 188,
х² + 4х + 4 - х² = 188,
4х = 184,
х = 46 - 1 число,
х+2 = 46+2 = 48 - 2 число
8x² - 9x(x+2) = 8x² - 9x*x -9x * 2 = 8x² - 9x² - 18x =
= -(9x² - 8x²) - 18x =- x² - 18x
(c-6)(c+4) =c*c +c*4 -6c -6*4 = c² +4c - 6c - 24 =
= c² - (6c - 4c) - 24 = c² -2c - 24
(2x + y)(x-7y) = 2x*x +2x*(-7y) +yx +y*(-7y) = 2x² -14xy +xy -7y² =
= 2x² - (14xy - xy) - 7y² = 2x² - 13xy - 7y²