Đáp án+Giải thích các bước giải:
`a)(x-y)(x^3+x^2y+xy^2+y^3)=x^4-y^4`
Ta có:`VT`:`(x-y)(x^3+x^2y+xy^2+y^3)`
`=x^4+x^3y+x^2y^2+xy^3-x^3y-x^2y^2-xy^3-y^4`
`=x^4+(x^3y-x^3y)+(x^2y^2-x^2y^2)+(xy^3-xy^3)-y^4`
`=x^4-y^4=VP(đpcm)`
`b)(a+b+c)(a^2+b^2+c^2-ab-bc-ca)=a^3+b^3+c^3-3abc`
Ta có:`VT:(a+b+c)(a^2+b^2+c^2-ab-bc-ca)`
`=a^3+ab^2+ac^2-a^2b-abc-a^2c+a^2b+b^3+bc^2-ab^2-b^2c-abc+a^2c+b^2c+c^3-abc-bc^2-ac^2`
`=a^3+(ab^2-ab^2)+(ac^2-ac^2)+(-a^2b+a^2b)+(-abc-abc-abc)+(-a^2c+a^2c)+b^3+(bc^2-bc^2)+(b^2c-b^2c)+c^3`
`=a^3+b^3+c^3-3abc=VP(đpcm)`
`c)(3a+2b-1)(a+5)-2b(a-2)=(3a+5)(a+3)+2(7b-10)`
Phân tích: `(3a+5)(a+3)+2(7b-10) =3a^2+9a+5a+15+14b-20`
`=3a^2+14a+14b-5`
Ta có`:VT`:`(3a+2b-1)(a+5)-2b(a-2)`
`=3a^2+15a+2ab+10b-a-5-2ab+4b`
`=3a^2+14a+14b-5=(3a+5)(a+3)+2(7b-10)=VP(đpcm)`
