Bµi 1. Thùc hiÖn phÐp tÝnh:
a) (5x – 2y)(x2 – xy + 1); b) (x – 1)(x + 1)(x + 2); c) x2y2(2x + y)(2x – y);
d) ( x – 1) (2x – 3); e) (x – 7)(x – 5); f) (x – )(x + )(4x – 1);
g) (x + 2)(1 + x – x2 + x3 – x4) – (1 – x)(1 + x +x2 + x3 + x4);
h) (2b2 – 2 – 5b + 6b3)(3 + 3b2 – b); i) (4a – 4a4 + 2a7)(6a2 – 12 – 3a3);
chỉ cần đáp án thôi
Đáp án+Giải thích các bước giải:
`a) (5x-2y)(x^2-xy+1)`
`=5x^3-5x^2y+5x-2x^2y+2xy^2-2y`
`=5x^3-7x^2y+2xy^2+5x-2y`
`b) (x-1).(x+1)(x+2)`
`=(x^2-1).(x+2)`
`=x^3+2x^2-x-2`
`c) x^2y^2(2x+y)(2x-y)`
`=x^2y^2(4x^2-y^2)`
`=4x^4y^2-x^2y^4`
`d) (x-1)(2x-3)`
`=2x^2-3x-2x+3`
`=2x^2-5x+3`
`e) (x-7)(x-5)`
`=x^2-5x-7x+35`
`= x^2 – 12x+35`
`f) (x-1/2)(x+1/2)(4x-1)`
`=(x^2-1/4)(4x-1)`
`=4x^3-x^2-x+1/4`
`g) (x+2).(1+x-x^2+x^3-x^4)-(1-x)(1+x+x^2+x^3+x^4)`
`=(x+x^2-x^3+x^4-x^5+2+2x-2x^2+2x^3-2x^4)-(1+x+x^2+x^3+x^4-x-x^2-x^3-x^4-x^5)`
`=x+x^2-x^3+x^4-x^5+2+2x-2x^2+2x^3-2x^4-1-x-x^2-x^3-x^4+x+x^2+x^3+x^4+x^5`
`=-x^4+x^3-x^2+3x+1`
`h) (2b^2-2-5b+6b^3)(3+3b^2-b)`
`=6b^2+6b^4-2b^3-6-6b^2+2b-15b-15b^3+5b^2+18b^3+18b^5-6b^4`
`=18b^5+b^3+5b^2-13b-6`
`i) (4a-4a^4+2a^7).(6a^2-12-3a^3)`
`=24a^3-48a-12a^4-24a^6+48a^4+12a^7+12a^9-24a^7-6a^10`
`=-6a^10+12a^9-12a^7-24a^6+24a^3`