`a)``(a+b)^{3}+(a-b)^{3}=2a(a^{2}+3b^{2})`
`↔[(a+b)+(a-b)][(a+b)^{2}-(a+b)(a-b)+(a-b)^{2}]=2a^{3}+6ab^{2}`
`↔(a+b+a-b)(a^{2}+2ab+b^{2}-a^{2}+b^{2}+a^{2}-2ab+b^{2})=2a^{3}+6ab^{2}` `↔2a(a^{2}+3b^{2})=2a^{3}+6ab^{2}`
`↔2a^{3}+6ab^{2}=2a^{3}+6ab^{2}`
`⇒VT=2a^{3}+6ab^{2}`
`VP=2a^{3}+6ab^{2}`
Vậy `VT=VP`
`⇒(a+b)^{3}+(a-b)^{3}=2a(a^{2}+3b^{2})` `(đpcm)`
`b)``(a+b)^{3}-(a-b)^{3}=2b(b^{2}+3a^{2})`
`↔[(a+b)-(a-b)][(a+b)^{2}+(a+b)(a-b)+(a-b)^{2}]=2b^{3}+6a^{2}b`
`↔(a+b-a+b)(a^{2}+2ab+b^{2}+a^{2}-b^{2}+a^{2}-2ab+b^{2})=2b^{3}+6a^{2}b` `↔2b(3a^{2}+b^{2})=2b^{3}+6a^{2}b`
`↔2b^{3}+6a^{2}b=2b^{3}+6a^{2}b`
`⇒VT=2b^{3}+6a^{2}b`
`VP=2b^{3}+6a^{2}b`
Vậy` VT=VP`
`⇒(a+b)^{3}-(a-b)^{3}=2b(b^{2}+3a^{2})``(đpcm)`
