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Question

Verify the following :

(i) 37×(56+1213)=(37×56)+(37×1213)
(ii) 154×(37+125)=(154×37)+(154×125)
(iii) (83+1312)×56=(83×56)+(1312×56)
(iv) 167×(89+76)=(167×89)+(167×76)

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Solution

(i) L.H.S.=37×(56+1213)

=37×(65+7278)=37×13778=411546

R.H.S.=(37×56)+(37×1213)

=3×57×6+3×127×13=1542+3691

=195+216546=411546

L.H.S.=R.H.S.

(ii) L.H.S.=154×(37+125)

=154×(158435)

=154×6935=1035140

R.H.S.=(154×37)+(154×125)

=15×34×7+15×(12)4×5

=4528+18020=225+1260140=1035140

L.H.S.=R.H.S.

(iii) L.H.S.=(83+1312)×56

=321312×56=4512×56=22572

R.H.S.=(83×56)+(1312×56)

=8×53×6+13×512×6=4018+6572

=160+(65)72=1606572

=22572

L.H.S.=R.H.S.

(iv) L.H.S.=167×(89+76)

=167×(16+(21)18)=167×3718

=16×377×18=592126

R.H.S.=(167×89)+(167×76)

=16×(8)7×9+16×(7)7×6=12863+11242

=256+336126=592126

L.H.S.=R.H.S.


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