Q1 of 105 Page 274

Factories the following expression-

l4 + 4l2m2 + 4m4

In given expression


1st and last terms are perfect square


⇒ l4 = l2 × l2


⇒ m4 = m2 × m2


And the middle expression is in form of 2ab


4l2m2 = 2 × l2 × m2


∴ l2 × l2 + 2 × m2 × l2 + m2 × m2


Gives (a + b)2 = a2 + 2ab + b2


⇒ In l4 + 4l2m2 + m4


a = l2 and b = m2;


∴ l4 – 4l2m2 + m4 = (l2-m2)2


Hence the factors of l4 + 4l2m2 + 4m4 are (l2-m2)and (l2-m2)


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