Question

(Find the LCM of): ( a2-a-6 and a2-9​

Answer 1

Answer:

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Step-by-step explanation:

We first factorize the given binomials 3(a−1),2(a−1)2 and a2−1 as shown below:

3(a−1)=3×(a−1)2(a−1)2=2×(a−1)×(a−1)a2−1=a2−12=(a−1)×(a+1)(∵x2−y2=(x−y)(x+y))

Now multiply all the factors, using each common factor only once, therefore, the LCM is:

3×2×(a−1)×(a−1)×(a+1)=6(a−1)2(a+1)

Hence, the LCM of 3(a−1),2(a−1)2 and a2−1 is 6(a−1)2(a+1).