`#Sad`
`1)`
`\text{→Chứng minh:}`
`(a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ac`
`\text{Ta có:}`
`\text{VT}` `= (a+b+c)^2`
`= [(a+b)+c]^2`
`= (a+b)^2+2c(a+b)+c^2`
`= a^2+2ab+b^2+2ac+2bc+c^2`
`= a^2+b^2+c^2+2ab+2bc+2ac` `=` `\text{VP}` `\text{(→đpcm)}`
`\text{→Áp dụng:}` `(A+B)^2 = A^2+2AB+B^2`
`2)`
`\text{→Chứng minh:}`
`(a^2+b^2)^2-4a^2b^2 = (a+b)^2(a-b)^2`
`\text{Ta có:}`
`\text{VT}` `= (a^2+b^2)^2-4a^2b^2`
`= (a^2+b^2-2ab)(a^2+b^2+2ab)`
`= (a^2-2ab+b^2)(a^2+2ab+b^2)`
`= (a-b)^2(a+b)^2` `=` `\text{VP}` `\text{(→đpcm)}`
`\text{→Áp dụng:}` `A^2-B^2 = (A-B)(A+B)`
`b)`
`(a^2+b^2)(x^2+y^2) = (ax-by)^2+(bx+ay)^2`
`\text{Ta có:}`
`\text{VP}` `= (ax-by)^2+(bx+ay)^2`
`= a^2x^2-2axby+b^2y^2+b^2x^2+2axby+a^2y^2`
`= (a^2x^2+b^2x^2)+(b^2y^2+a^2y^2)`
`= x^2(a^2+b^2)+y^2(b^2+a^2)`
`= (x^2+y^2)(a^2+b^2)` `=` `\text{VT}` `\text{(→đpcm)}`
`\text{→Áp dụng:}`
`(A-B)^2 = A^2-2AB+B^2`
`(A+B)^2 = A^2+2AB+B^2`
