1) а) = р² + 16р + 64
б) = 100х² -60ху + 9у²
в) = х² - 81
г) = 49n² - 16m²
2) а) = (4 -с)4+с)
б) = (р +1)²
в) = ( 3m -5)(3m +5)
г) = (6m +2n)²
3)(a - 10)² -(a -5)(a +5) = a² -20a +100 - a² +25 = -20a + 125
4) (2x -7)(x +1) +3(4x -1)(4x +1) = 2(5x -2)² - 53
2x² -7x +2x -7 +3(16x² -1) = 2(25x² -20x +4) -53
2x² -5x -7 +48x² -3 = 50x² -40x +8 -53
35x = -35
x = -1
5) (3a +1)² - (a -6)² = (3a +1 -a +6)(3a +1 +a -6) = (2a +7)(4a -5)
6)(2-x)(2 +x)(4 +x²) + (6 -x²)² = (4 -x²)(4 +x²) +36 -12x + x⁴=
=16 - x⁴+36 -12x + x⁴ = 52 -12x= 52 -12*(-1/2) = 52 +6 = 58
7) x² - 18x + 84 = x² -2*x*9 +81 +3 = (x -9)² -3 > 0