Bài 1:
a) `A= (2/3 x^3 y^3 ). ( 1/2 x y^2)^3 . (-8/5 x^2)`
`A= 2/3 . x^3y^3 ( 1/2)^3 x^3 (y^2)^3 (-8/5) x^2`
`A=2/3 . x^3y^3 . 1/8 x^3y^6 . (-8/5) x^2`
`A= (-8/5 . 2/3 .1/8) . (x^3 x^3x^2) (y^3 y^6)`
`A= -2/15 x^8 y^9`
Hệ số: `-2/15`
Phần biến: `x^8y^9`
Bậc: `17`
b) Thay `x = 2; y= -1/2` vào `A` ta được:
`A= -2/15 . 2^8 . (- 1/2)^9`
`A= -2/15. 256 . (-1/512)`
`A= -512/15 . (- 1/512)`
`A=1/15`
Vậy `A= 1/15` khi `x=2; y= -1/2`
Bài 2:
a) `P(x)= x^4 + 3x^3 -x + 1/2 - x^3 -4x`
`= x^4 + (3x^3 - x^3) - (x + 4x) + 1/2`
`= x^4 + 2x^3 - 5x + 1/2`
Sắp xếp: `P(x)= x^4 + 2x^3 - 5x + 1/2`
`Q(x)= 3/2 -4x^3 + x^4 -2x-3x + 2x^3`
`= 3/2 - (4x^3 - 2x^3) + x^4 - (2x + 3x)`
`= 3/2 - 2x^3 + x^4 - 5x`
Sắp xếp: ` Q(x) =x^4 - 2x^3 - 5x + 3/2`
b) `P(x) + Q(x) = x^4 + 2x^3 - 5x + 1/2 + x^4 - 2x^3 - 5x + 3/2`
`= (x^4 + x^4) + (2x^3 - 2x^3) - (5x + 5x) +( 1/2 + 3/2)`
`= 2x^4 - 10x + 2`
`P(x) - Q(x)= (x^4 + 2x^3 - 5x + 1/2) - ( x^4 - 2x^3 - 5x + 3/2)`
`= x^4 + 2x^3 - 5x + 1/2 - x^4 + 2x^3 + 5x - 3/2`
`= (x^4 - x^4) + (2x^3 + 2x^3) - (5x - 5x) + (1/2 - 3/2)`
`= 4x^3 -1`
Vậy `P(x) + Q(x)= 2x^4 - 10x + 2` ; `P(x) - Q(x)= 4x^3 -1`
