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Expand (i) (4a+5b)^3 (ii) (3a-2b)^3...

Expand (i)` (4a+5b)^3`
(ii) ` (3a-2b)^3`

Text Solution

Verified by Experts

(i) Putting `4a=x,and 5b=y`, we get
` (4a +5b)^3=(x+y)^3`
`=x^3+y^3xy(x+y)`
`=(4a)^3+(5b)^3+(3xx4a xx 5b)(4a+5b)`
` =64a^3+125b^3+60ab(4a+5b)`
`=64a^3+125b^3+24a^2b+300ab^2`.
(ii) Putting `3a=x and 2b =y`, we get
` 3a-2b)^3=(x-y)^3`
`=x^3-y^3-3xy (x-y)`
`=(3a)^3-(2b)^3-(3xx3a xx 2b) (3a- 2b)`
`=27a^3=8b^3-18ab(3a-2b)`
`=27 a^3-8b^3-54a^2b+36ab^2`.
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