Q6 of 65 Page 137

Let us factorise the following algebraic expressions:

p4 – 11p2q2 + q4

Given, p4 – 11p2q2 + q4


⇒ (p2)2 – 11p2q2 + (q2)2


⇒ (p2)2 – 2p2q2 – 9 p2q2 + (q2)2


⇒ (p2)2 – 2p2q2 + (q2)2 – 9 p2q2


⇒ (p2 – q2)2 – (3pq)2


⇒ ((p2 – q2) – 3pq)((p2 – q2) + 3pq)


⇒ (p2 – q2 – 3pq)(p2 – q2 + 3pq)


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