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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)LHS=37×56+1213=37×65 +7278=37×13778=137182RHS=37×56+1213×37=3×57×6+12×313×7=1542+3691=195+216546=411546=137182

∴ ​37×(56+1213)=(37×56)+(37×1213)

(ii)LHS=-154×(37+-125)=-154×(15-8435)=-154×-6935=(-15)×(-69)140=1035140=20728RHS=(-154×37)+(-154×-125)=(-15)×34×7+(-15)×(-12)4×5=-4528+18020=-225+1260140=1035140=20728 -154×(37+-125)=(-154×37)+(-154×-125)

(iii)

(-83+-1312)×56=(-83×56)+(-1312×56)LHS=(-83+-1312)×56=-32-1312×56=-4512×56=-45×512×6=-22572=-225÷972÷9=-258RHS=(-83×56)+(-1312×56)=-8×53×6+(-13)×512×6=-4018+-6572=-160-6572=-22572=-225÷972÷9=-258 (-83+-1312)×56=(-83×56)+(-1312×56)

(iv)

-167×(-89+-76)=(-167×-89)+(-167×-76)LHS=-167×(-89+-76)=-167×(-16-2118)=-167×-3718=592126=29663RHS=(-167×-89)+(-167×-76)=12863+11242=256+336126=592126=29663 -167×(-89+-76)=(-167×-89)+(-167×-76)

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