Q11 of 25 Page 8

Find (a + b)4 - (a – b)4. Hence, evaluate .


(a + b)4 -(a - b)4
= [4C0a4 + 4C1a3b + 4C2a2b2 + 4C3ab3 + 4C4b4] - [4C0a4 + 4Cla3b + 4C2a2b2 - 4C3 ab3 + 4C4 b4] = 2 × 4C1 a3b + 2 × 4C3 ab3
= 2[4a3b + 4ab3]
= 8ab [a2 + b2]
Thus, ( +)4 - ( - )4
= 8 . [3 + 2] = 8(5) = 40

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