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Write the following in expanded form: (1...

Write the following in expanded form: `(1/4a-1/2b+1)^2` (ii) `(-2x+5y-3z)^2`

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(i) `(1/4a-1/2b+1)^2`
`((a/4)−(b/2)+1)^2`
Using the identity, `(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc`:
`=(a/4)^2+(−b/2)^2+1^2+2×(a/4)(−b/2)+2(−b/2)×1+2×1×(a/4)`
`=(a^2/16)+(b^2/4)+1−((ab)/4)−b+(a/2)`
`therefore (1/4a-1/2b+1)^2=(a^2/16)+(b^2/4)+1−((ab)/4)−b+(a/2)`

(ii) `(-2x+5y-3z)^2`
Using the identity, `(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc`:
`=(−2x)^2+(5y)^2+(−3z)^2+2(−2x)(5y)+2(5y)(−3z)+2(−2x)(−3z)`
`=4x^2+25y^2+9z^2−20xy−30yz+12zx`
`therefore (-2x+5y-3z)^2=4x^2+25y^2+9z^2−20xy−30yz+12zx`
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