Hướng dẫn giải:
`1.1,` `(x+y+z)^2`
`=x^2+y^2+z^2+2xy+2xz+2yz`
`1.2,` `(x-y+z)^2`
`=x^2+(-y)^2+z^2+2x.(-y)+2xz+2.(-y)z`
`=x^2+y^2+z^2+2x.(-y)+2xz+2.(-y)z``
`=x^2+y^2+z^2-2xy+2xz+2.(-y)z`
`=x^2+y^2+z^2-2xy+2xz-2yz`
`2,` `(x-y-z)^2`
`=x^2+(-y)^2+(-z)^2+2x(-y)+2x(-z)+2(-y)(-z)`
`=x^2+y^2+z^2+2x(-y)+2x(-z)+2(-y)(-z)`
`=x^2+y^2+z^2-2xy+2x(-z)+2(-y)(-z)`
`=x^2+y^2+z^2-2xy-2xz+2(-y)(-z)`
`=x^2+y^2+z^2-2xy-2xz+2yz`
`3,` `(a^2+2a+3)(a^2+2a-3)`
`=(a^2+2a)^2-9`
`=a^4+4a^3+4a^2-9`
`4,` `(a^2+2a+3)(a^2-2a-3)`
`=a^4-(2a+3)^2`
`=a^4-(4a^2+12a+9)`
`=a^4-4a^2-12a-9`
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Công thức:
`@` `(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc`
`@` `(-).(-)=(+)`
`@` `(a-b)(a+b)=a^2-b^2`
`@` `(a+b)^2=a^2+2ab+b^2`
