Hướng dẫn trả lời:
Câu 1:
a) `2x^2.(3x^2 - 5x + 4) - (6x^4 - 10x^3) + 4.(505 - 2x^2).`
`= 2x^2. 3x^2 - 2x^2 .5x + 2x^2 .4 - 6x^4 + 10x^3 + 4.505 - 4.2x^2.`
`= 6x^4 - 10x^3 + 8x^2 - 6x^4 + 10x^3 + 2020 - 8x^2.`
`= (6x^4 - 6x^4) + (- 10x^3 + 10x^3) + (8x^2 - 8x^2) + 2020.`
`= 2020.`
b) `-x^2.(-2x^2 + 3x - 1) - (7x^4 - 5x^3).`
`= -x^2.(-2x^2) - x^2 .3x - x^2.(- 1) - 7x^4 + 5x^3.`
`= 2x^4 - 3x^3 + x^2 - 7x^4 + 5x^3.`
`= (2x^4 - 7x^4) + (- 3x^3 + 5x^3) + x^2.`
`= - 5x^4 + 2x^3 + x^2.`
c) `-2x^2.(3x - 1/4 - 2x^3) - (4x^5 - 6x^3).`
`= -2x^2. 3x - 2x^2.(-1/4) - 2x^2.(-2x^3) - 4x^5 + 6x^3.`
`= -6x^3 + 1/2x^2 + 4x^5 - 4x^5 + 6x^3.`
`= (4x^5 - 4x^5) + (-6x^3 + 6x^3) + 1/2x^2.`
`= 1/2x^2.`
d) `(-3x + 2).(3x - 4) + (3x - 1).(3x + 1).`
`= -3x.(3x - 4) + 2.(3x - 4) + 3x.(3x + 1) - 1.(3x + 1).`
`= -9x^2 + 12x + 6x - 8 + 9x^2 + 3x - 3x - 1.`
`= (-9x^2 + 9x^2) + (12x + 6x + 3x - 3x) + (- 8 - 1).`
`= 18x - 9.`
Câu 2:
a)
1) `(1/2x + 3)^2.`
`= (1/2x)^2 + 2. 1/2x.3 + 3^2.`
`= 1/4x^2 + 3x + 9.`
2) `(x - 3)^3.`
`= x^3 - 3.x^2 .3 + 3.x.3^2 - 3^3.`
`= x^3 - 9x^2 + 27x - 27.`
b) `Q = -3.(x + 1).(3x + 2) + 9x^2 + 3.(5x + 15).`
`= -3.(3x^2 + 5x + 2) + 9x^2 + 15x + 45.`
`= -9x^2 - 15x - 6 + 9x^2 + 15x + 45.`
`= (-9x^2 + 9x^2) + (- 15x + 15x) + (- 6 + 45).`
`= 39.`
c) Ta có: `D = x^2 - 14x + 49.`
`= x^2 - 2.x.7 + 7^2.`
`= (x - 7)^2.`
Với `x = 27`, ta có: `D = (27 - 7)^2.`
`= 20^2.`
`= 400.`
