Hướng dẫn trả lời:
Bài 4:
1) `A = -3xcdot(x + 2)^2 + (x + 3)cdot(x - 1)cdot(x + 1) - (2x - 3)^2`
`= -3xcdot(x^2 + 2cdotxcdot2 + 2^2) + (x + 3)cdot(x^2 - 1^2) - [(2x)^2 - 2cdot2xcdot3 + 3^2]`
`= -3xcdot(x^2 + 4x + 4) + (x + 3)cdot(x^2 - 1) - (4x^2 - 12x + 9)`
`= -3xcdot(x^2 + 4x + 4) + xcdot(x^2 - 1) + 3cdot(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 + 12x - x) + (- 3 - 9)`
`= -2x^3 - 13x^2 - x - 12`
Giải thích:
Áp dụng HĐT:
`(A + B)^2 = A^2 + 2AB + B^2`
`A^2 - B^2 = (A + B)cdot(A - B)`
`(A - B)^2 = A^2 - 2AB + B^2`
2) `B = (x - 3)cdot(x + 3)cdot(x + 2) - (x - 1)cdot(x^2 - 3) - 5xcdot(x + 4)^2 - (x - 5)^2`
`= (x^2 - 3^2)cdot(x + 2) - (x - 1)cdot(x^2 - 3) - 5xcdot(x^2 + 2cdotxcdot4 + 4^2) - (x^2 - 2cdotxcdot5 + 5^2)`
`= (x^2 - 9)cdot(x + 2) - (x - 1)cdot(x^2 - 3) - 5xcdot(x^2 + 8x + 16) - (x^2 - 10x + 25)`
`= x^2cdot(x + 2) - 9cdot(x + 2) - xcdot(x^2 - 3) + 1cdot(x^2 - 3) - 5xcdot(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 - x^2 - 40x^2) + (- 9x + 3x - 80x + 10x) + (- 18 - 3 - 25)`
`= - 5x^3 - 38x^2 - 76x - 46`
Giải thích:
Áp dụng HĐT:
`(A + B)^2 = A^2 + 2AB + B^2`
`A^2 - B^2 = (A + B)cdot(A - B)`
`(A - B)^2 = A^2 - 2AB + B^2`
3) `C = 2xcdot(x - 4)^2 - (x + 5)cdot(x - 2)cdot(x + 2) + 2cdot(x + 5)^2 - (x - 1)^2`
`= 2xcdot(x^2 - 2cdotxcdot4 + 4^2) - (x + 5)cdot(x^2 - 2^2) + 2cdot(x^2 + 2cdotxcdot5 + 5^2) - (x^2 - 2cdotxcdot1 + 1^2)`
`= 2xcdot(x^2 - 8x + 16) - (x + 5)cdot(x^2 - 4) + 2cdot(x^2 + 10x + 25) - (x^2 - 2x + 1)`
`= 2xcdot(x^2 - 8x + 16) - xcdot(x^2 - 4) - 5cdot(x^2 - 4) + 2cdot(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 + 69`
Giải thích:
Áp dụng HĐT:
`(A + B)^2 = A^2 + 2AB + B^2`
`A^2 - B^2 = (A + B)cdot(A - B)`
`(A - B)^2 = A^2 - 2AB + B^2`
4) `D = (x + 5)^2 - 4xcdot(2x + 3)^2 - (2x - 1)cdot(x + 3)cdot(x - 3)`
`= (x^2 + 2cdotxcdot5 + 5^2) - 4xcdot[(2x)^2 + 2cdot2xcdot3 + 3^2] - (2x - 1)cdot(x^2 - 3^2)`
`= (x^2 + 10x + 25) - 4xcdot(4x^2 + 12x + 9) - (2x - 1)cdot(x^2 - 9)`
`= (x^2 + 10x + 25) - 4xcdot(4x^2 + 12x + 9) - 2xcdot(x^2 - 9) + 1cdot(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`
Giải thích:
Áp dụng HĐT:
`(A + B)^2 = A^2 + 2AB + B^2`
`A^2 - B^2 = (A + B)cdot(A - B)`
`(A - B)^2 = A^2 - 2AB + B^2`
Đáp án:
1) `A = -2x^3 - 13x^2 - x - 12`
2) `B = - 5x^3 - 38x^2 - 76x - 46`
3) `C = x^3 - 20x^2 + 58x + 69`
4) `D = - 18x^3 - 46x^2 - 8x + 16`
