Đáp án:
Giải thích các bước giải:
1/
-3x(x + 2)^2 + (x + 3)(x - 1)(x + 1) - (2x - 3)^2
= -3x(x^2 + 4x + 4) + (x + 3)(x^2 - 1) - (4x^2 - 12x + 9)
= -3x^3 - 12x^2 - 12x + x^3 - x + 3x^2 - 3 - 4x^2 + 12x - 9
= (-3x^3 + x^3) + (-12x^2 + 3x^2 - 4x^2) +(-12x - x + 12x) + (-3 + 9)
= -2x^3 - 13x^2 - x + 6
2/
(x - 3)(x + 3)(x + 2) - (x - 1)(x^2 - 3) - 5x (x + 4)^2 - (x - 5)^2
= (x^2 - 9)(x + 2) - (x^3 - 3x - x^2 + 3) - 5x (x^2 + 8x + 16) - (x^2 - 10x + 25)
= (x^3 + 2x^2 - 9x - 18) - (x^3 - 3x - x^2 +3) - 5x^3 - 40x^2 - 80x - (x^2 - 10x + 25)
= (x^3 - x^3 - 5x^3) + ( 2x^2 - x^2 - 40x^2 - x^2) + (-9x + 3x - 80x + 10x) + (-18 -3 -25)
= -5x^3 - 40x^2 - 58x - 46
3/
2x(x - 4)^2 - (x + 5)(x - 2)(x + 2) + 2(x + 5)^2 - (x - 1)^2
= 2x(x^2 - 8x + 16) - (x + 5)(x^2 - 4) + 2(x^2 + 10x + 25) - (x^2 - 2x + 1)
= 2x^3 - 16x^2 + 32x - (x^3 - 4x + 5x^2 - 20) + 2x^2 + 20x + 50 - x^2 + 2x -1
= (2x^3 - x^3) + (-16x^2 - 5x^2 + 2x^2 - x^2) + (32x + 4x +20x+2x) + (-20 + 50 - 1)
= x^3 - 20x^2 + 58x + 29
4/
(x+5)^2 - 4x(2x + 3)^2 - (2x - 1)(x + 3)(x - 3)
= (x^2 + 10x + 25) - 4x(4x^2 + 12x + 9) - (2x - 1)(x^2 - 9)
= (x^2 + 10x + 25) - (16x^3 + 48x^2 + 36x) - (2x^3 - 18x - x^2 + 9)
= (-16x^3 - 2x^3) + (x^2 - 48x^2 + x^2) + (10x - 36x + 18x) + (25 - 9)
= -18x^3 - 46x^2 - 8x + 16
5/
-2(3x + 2)(3x - 2) + 5(x + 2)^2 - (x - 1)(2x + 1)(2x + 1)
= -2(9x^2 - 4) + 5(x^2 + 4x + 4) - (x - 1)(2x + 1)^2
= (-18x^2 + 8) + (5x^2 + 20x + 20) - (x - 1)(4x^2 + 4x + 1)
= (-18x^2 + 8) + (5x^2 + 20x + 20) - (4x^3 + 4x^2 + x - 4x^2 - 4x - 1)
= -4x^3 + (-18x^2 + 5x^2 - 4x^2 + 4x^2) + (20x - x + 4x) + (8 + 20 + 1)
= -4x^3 -13x^2 + 23x + 29
6/
(7x - 8)(7x + 8) - 10(2x + 3)^2 + 5x(3x - 2)^2 - 4x(x - 5)^2
= (49x^2 - 64) - 10(4x^2 + 12x + 9) + 5x(9x^2 - 12x + 4) - 4x(x^2 - 10x + 15)
= (49x^2 - 64) - 40x^2 - 120x - 90 + 45x^3 - 60x^2 + 20x - 4x^3 + 40x^2 - 60x
= (45x^3 - 4x^3) + (49x^2 - 40x^2 - 60x^2 + 40x^2) + (-120x + 20x - 60x) + (-64 - 90)
= 41x^3 - 11x^2 - 160x - 154
7/
(x^2 - 3)(x^2 + 3) - 5x^2(x + 1)^2 - (x^2 - 3x)(x^2 - 2x) + 4x(x + 2)^2
= (x^4 - 9) - 5x^2(x^2 + 2x + 1) - (x^4 - 2x^3 - 3x^3 + 6x^2) + 4x(x^2 + 4x + 4)
= (x^4 - 9) - 5x^4 - 10x^3 - 5x^2 - x^4 + 2x^3 + 3x^3 - 6x^2 + 4x^3 + 16x^2 + 16x
= (x^4 - 5x^4 - x^4) + (-10x^3 +2x^3 + 3x^3 + 4x^3) + (-5x^2 - 6x^2 + 16x^2) + 16x - 9
= -5x^4 - x^3 + 5x^2 + 16x - 9
