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Write the following in expanded form: `(9x+2y+z)^2` (ii) `(3x+2y-z)^2`

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(i) `(9x+2y+z)^2`
Using the identity `(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ac`:
`=81x^2+4y^2+z^2+36xy+4yz+18xz`
`therefore (9x+2y+z)^2=81x^2+4y^2+z^2+36xy+4yz+18xz`

(ii) `(3x+2y-z)^2`
`=[3x+2y+(−z)]^2`
Using the identity `(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ac`:
`=(3x)^2+(2y)^2+(−z)^2+2×3x×2y+2×2y×(−z)+2×3x×(−z)`
`=9x^2+4y^2+z^2+12xy−4yz−6xz`
`therefore (3x+2y-z)^2=9x^2+4y^2+z^2+12xy−4yz−6xz`
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