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Question

Simplify
(i) 3-11 3+11
(ii) -3+5 -3-5
(iii) 3-32
(iv) 5-32
(v) 5+7 2+5
(vi) 5-2 2-3

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Solution

(i) 3-11 3+11

=32-112 [a-ba+b=a2-b2]=9-11=-2

(ii) -3+5 -3-5

=-32-52 [a+ba-b=a2-b2]=9-5=4

(iii) 3-32

=32+32-2×3×3 [a-b2=a2+b2-2ab]=9+3-63=12-63

(iv) 5-32

=52+32-2×53 [a-b2=a2+b2-2ab]=5+3-215=8-215
=5×2-5×3-2×2+2×3 =10-15-2+6

(v) 5+7 2+5

5+72+5=5×2+5×5+7×2+7×5=10+55+27+35

(vi) 5-2 2-3

5-22-3=5×2-5×3-2×2+2×3 =10-15-2+6

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