Question

find the lcm of a2 + 4a - 12, a2 -5a +6 whose gcd is a-2

Answer 1

Answer:

First expression = x2 - 4

                      = x2 - 22, by using the formula of a2 – b2 

                      = (x + 2) (x - 2), we know a2– b2 = (a + b) (a – b)

Second expression = x2 + 2x

                          = x(x + 2), by taking common ‘x’    

The common factor of the two expressions is ‘(x + 2)’.

The extra common factor in the first expression is (x - 2) and in the second expression is x.

Therefore, the required L.C.M = (x + 2) ×(x - 2) × x

                                        = x(x + 2) (x - 2)

Step-by-step explanation:

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