Question

`the factor of 3a^2 - 108b^2 are`
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Answer 1

The factors are 3, a- 6b and a + 6b

Step-by-step explanation:

Given

`3a^2 -108b^2`

Required

The factors

`3a^2 -108b^2 =`

Factor 3 out

`3a^2 -108b^2 = 3(a^2 - 36b^2)`

Express 36 as
`6^2`

`3a^2 -108b^2 = 3(a^2 - 6^2*b^2)`

`3a^2 -108b^2 = 3(a^2 - (6b)^2)`

Apply difference of two squares

`3a^2 -108b^2 = 3(a - 6b)(a + 6b)`

So, the factors are 3, a- 6b and a + 6b