Đáp án + Giải thích các bước giải:
Bài `8` :
`b)` `VT=a^4+b^4=(a^2)^2+(b^2)^2`
`=(a^2+b^2)^2-2a^2b^2=VP`
`c)` `VT=a^6+b^6=(a^2)^3+(b^2)^3`
`=(a^2+b^2)[(a^2)^2-a^2b^2+(b^2)^2]`
`=(a^2+b^2)[(a^2+b^2)^2-2a^2b^2-a^2b^2]`
`=(a^2+b^2)[(a^2+b^2)^2-3a^2b^2]=VP`
`d)` `VT = a^6-b^6=(a^2)^3-(b^2)^3`
`=(a^2-b^2)[(a^2)^2+a^2b^2+(b^2)^2]`
`=(a^2-b^2)[(a^2+b^2)^2-2a^2b^2+a^2b^2]`
`=(a^2-b^2)[(a^2+b^2)^2-a^2b^2]=VP`
`e)` `VT = x^4+y^4+(x+y)^4`
`=x^4+y^4+[(x+y)^2]^2`
`=x^4+y^4+(x^2+2xy+y^2)^2`
`=x^4+y^4+(x^2+2xy+y^2)(x^2+2xy+y^2)`
`=x^4+y^4+x^4+2x^3y+x^2y^2+2x^3y+4x^2y^2+2xy^3+x^2y^2+2xy^3+y^4`
`=(x^4+x^4)+(y^4+y^4)+(2x^3y+2x^3y)+(x^2y^2+4x^2y^2+x^2y^2)+(2xy^3+2xy^3)`
`=2x^4+2y^4+4x^3y+6x^2y^2+4xy^3`
`=2(x^4+y^4+2x^3y+3x^2y^2+2xy^3)`
`=2(x^2+xy+y^2)^2=VP`
Bài `9` :
`(a+b)^2=2(a^2+b^2)`
`<=>a^2+2ab+b^2=2a^2+2b^2`
`<=>a^2+2ab+b^2-2a^2-2b^2=0`
`<=>-a^2+2ab-b^2=0`
`<=>a^2-2ab+b^2=0`
`<=>(a-b)^2=0`
`<=>a-b=0<=>a=b` (đpcm).
