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Question

Factorize each of the following algebraic expression:
49 − a2 + 8ab − 16b2

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Solution

49-a2+8ab-16b2=49-(a2-8ab+16b2)=49-[a2-2×a×4b+(4b)2]=72-(a-4b)2=[7-(a-4b)][7+(a-4b)]=(7-a+4b)(7+a-4b)=-(a-4b-7)(a-4b+7)=-(a-4b+7)(a-4b-7)

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