Đáp án:
`a, CM: (x^3 + x^2 y + xy^2 + y^3)(x - y) = x^4 - y^4`
Ta có:
`VT = (x^3 + x^2 y + xy^2 + y^3)(x - y)`
`= [(x^3 + y^3) + (x^2 y + xy^2)](x - y)`
`= [(x + y)(x^2 - xy + y^2) + xy(x + y)](x - y)`
`= (x + y)(x^2 - xy + y^2 + xy)(x - y)`
`= [(x + y)(x - y)](x^2 + y^2)`
`= (x^2 - y^2)(x^2 + y^2)`
`= (x^2)^2 - (y^2)^2`
`= x^4 - y^4 = VP`
`→ đpcm`
`b, (a + b)(a^2 - ab + b^2) + (a - b)(a^2 + ab + b^2) = 2a^3`
Ta có:
`VT = (a + b)(a^2 - ab + b^2) + (a - b)(a^2 + ab + b^2)`
`= a^3 + b^3 + a^3 - b^3`
`= (a^3 + a^3) + (b^3 - b^3)`
`= 2a^3 = VP`
`→ đpcm`
`c, (x - 1)(x^2 + x + 1) = x^3 - x`
Đề sai:
Sửa: `(x - 1)(x^2 + x + 1) = x^3 - 1`
Ta có:
`VT = (x - 1)(x^2 + x + 1)`
`= x(x^2 + x + 1) - 1(x^2 + x + 1)`
`=x^3 + x^2 + x - x^2 - x - 1`
`= x^3 + (x^2 - x^2) + (x - x) - 1`
`= x^3 - 1= VP`
`→ đpcm`
