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Factorise the following expressions (i) (l + m)^2 − 4lm (Hint: Expand (l + m)^2 first) (ii) a^4 + 2a^2b^2 + b^4

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Factorise the following expressions

(i) (l + m)2 − 4lm (Hint: Expand (l + m)2 first)

(ii) a4 + 2a2b2 + b4

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(i) (l + m)2 − 4lm 

= l2 + 2lm + m2 − 4lm

= l2 − 2lm + m2

= (l − m)2     [(a − b)2 = a2 − 2ab + b2]

(ii) a4 + 2a2b2 + b4 

= (a2)2 + 2 (a2) (b2) + (b2)2

= (a2 + b2)2       [(a + b)2 = a2 + 2ab + b2]

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