Thực hiện các phép tính sau:
a. (x3 + 5×2 – 2x + 1)(x – 7)
b. (2×2 – 3xy + y2)(x + y)
c. (x – 2)(x2 – 5x + 1) – x(x2 + 11)
d. [(x2 – 2xy + 2y2)(x + 2y) – (x2 + 4y2)(x – y)] 2x
Thực hiện các phép tính sau: a. (x3 + 5×2 – 2x + 1)(x – 7) b. (2×2 – 3xy + y2)(x + y) c. (x – 2)(x2 – 5x + 1) – x(x2 + 11) d. [(x2 – 2xy + 2y2)(x + 2y
By Iris
`a) (x^3 + 5x^2 – 2x + 1)(x – 7)`
`= x^4 – 2x^3 – 37x^2 + 15x – 7`
`b) (2x^2 – 3xy + y^2)(x + y)`
`= 2x^3 – x^2y – 2xy^2 + y3`
`c) (x – 2)(x^2 – 5x + 1) – x(x^2 + 11)`
`= x^3 – 5x^2 + x – 2x^2 + 10x – 2 – x^3 – 11x`
`= – 7x^2 – 2`
`d) [(x^2 – 2xy + 2y^2)(x + 2y) – (x^2 + 4y^2)(x – y)] 2xy`
`= – 12x^2y^3 + 2x^3y^2 + 16xy`
Đáp án:
a,Ta có :
`(x^3 + 5x^2 – 2x + 1)(x – 7)`
` = x^4 + 5x^3 – 2x^2 + x – 7x^3 – 35x^2 + 14x – 7`
` = x^4 – 2x^3 – 37x^2 + 15x – 7`
b, `(2x^2 – 3xy + y^2)(x + y)`
` = 2x^3 – 3x^2y + y^2x + 2x^2y – 3xy^2 + y^3`
` = 2x^3 – x^2y – 2xy^2 + y^3`
c`(x – 2)(x^2 – 5x + 1) – x(x^2 + 11)`
` = x^3 – 5x^2 + x – 2x^2 + 10x – 2 – x^3 – 11x`
` = -7x^2 – 2`
d, `[(x^2 – 2xy + 2y^2)(x + 2y) – (x^2 + 4y^2)(x – y)].2x`
` = (x^3 – 2x^2y + 2y^2x + 2yx^2 – 4xy^2 + 4y^3 – x^3 – 4y^2x + x^2y + 4y^3].2x`
` = (8y^3 + x^2y – 6xy^2).2x`
` = 16y^3x + 2x^3y – 12x^2y^2`
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