Q2 of 65 Page 139

Let us factorize the following algebraic expressions:

729p6 – q6

We know, a2 – b2 = (a + b) (a – b)


Given,


729p6 – q6


= (27p3)2 – (q3)2


= (27p3 + q3) (27p3 – q3)


Now, a3 – b3 = (a – b)(a2 + ab + b2) and a3 + b3 = (a + b)(a2 – ab + b2)


= [(3p)3 + (q)3] [(3p)3 – (q)3]


= (3p + q)(3p2 – 3pq + q2) (3p – q)(3p2 + 3pq + q2)


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