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Question
Simplify the following products:
`(1/2a - 3b)(1/2a + 3b)(1/4a^2 + 9b^2)`
Solution
`(1/2a - 3b)(1/2a + 3b)(1/4a^2 + 9b^2)`
`=>[(1/2 a)^2 - (3b)^2][1/4 a^2 + 9b^2]` `[∵ (a + b)(a - b) = a^2 - b^2]`
`= [(1/4 a^2) -9b^2][1/2a^2 + 9b^2]` `[∵ (ab)^2 = a^2 - b^2]`
`= [1/4 a^2] - [9b^2]^2` `[∵ (a - b)(a + b) = a^2 - b^2]`
`= 1/16 a^4 - 81b^4`
`∴ (1/2 a - 3b)(1/2 a + 3b)(1/4 a^2 + 9b^2) = 1/16 a^4 - 81b^4`
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