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Question

Factorize the following algebraic expression:

(a25a)236

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Solution

Given : (a25a)236
=(a25a)262
Using the formula, x2y2=(x+y)(xy)
=(a25a+6)(a25a6)

Now, factorizing the expression :(a25a6)
On splitting its middle term, we get

a2+a6a6
=a(a+1)6(a+1)
=(a6)(a+1) .....(i)

Now, factorizing the expression : (a25a+6)
On splitting its middle term, we get

a22a3a+6
=a(a2)3(a2)
=(a3)(a2) .....(ii)

(a25a)236=(a25a+6)(a25a6)
=(a+1)(a6)(a2)(a3)

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