Question

(3k-4r-2m) 2-(3m+4r-2m) 2​

Answer 1

Answer:

(3k – 4r – 2m)2 -(3k + 4r – 2m)2 = [(3k)2 +(- 4r)2 + (- 2m)2 +{2 ×(3k)×(- 4r)} +{2 ×(- 4r)× (-2m)} +{2 ×(3k)×(- 2m)} ] - [(3k)2 + (4r)2 +(- 2m)2 +{2 ×(3k)×(4r)} +{2 × (4r)×(- 2m)} +{2 ×(3k)×(-2m)} ]

(3k – 4r – 2m)2 -(3k + 4r – 2m)2 = [(3k)2 +(- 4r)2 + (- 2m)2 +{2 ×(3k)×(- 4r)} +{2 ×(- 4r)× (-2m)} +{2 ×(3k)×(- 2m)} ] - [(3k)2 + (4r)2 +(- 2m)2 +{2 ×(3k)×(4r)} +{2 × (4r)×(- 2m)} +{2 ×(3k)×(-2m)} ]{ ∵(a + b +c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac }

(3k – 4r – 2m)2 -(3k + 4r – 2m)2 = [(3k)2 +(- 4r)2 + (- 2m)2 +{2 ×(3k)×(- 4r)} +{2 ×(- 4r)× (-2m)} +{2 ×(3k)×(- 2m)} ] - [(3k)2 + (4r)2 +(- 2m)2 +{2 ×(3k)×(4r)} +{2 × (4r)×(- 2m)} +{2 ×(3k)×(-2m)} ]{ ∵(a + b +c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac }= [ 9k2 + 16r2 + 4m2+{ – 24kr} +{16rm } +{ – 12km } ] - [ 9k2 + 16r2 + 4m2 +{24kr } +{– 16rm } + { – 12km } ]

(3k – 4r – 2m)2 -(3k + 4r – 2m)2 = [(3k)2 +(- 4r)2 + (- 2m)2 +{2 ×(3k)×(- 4r)} +{2 ×(- 4r)× (-2m)} +{2 ×(3k)×(- 2m)} ] - [(3k)2 + (4r)2 +(- 2m)2 +{2 ×(3k)×(4r)} +{2 × (4r)×(- 2m)} +{2 ×(3k)×(-2m)} ]{ ∵(a + b +c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac }= [ 9k2 + 16r2 + 4m2+{ – 24kr} +{16rm } +{ – 12km } ] - [ 9k2 + 16r2 + 4m2 +{24kr } +{– 16rm } + { – 12km } ]= [ 9k2 + 16r2 + 4m2 – 24kr + 16rm – 12km ] - [ 9k2 + 16r2 + 4m2 + 24kr – 16rm – 12km ]

(3k – 4r – 2m)2 -(3k + 4r – 2m)2 = [(3k)2 +(- 4r)2 + (- 2m)2 +{2 ×(3k)×(- 4r)} +{2 ×(- 4r)× (-2m)} +{2 ×(3k)×(- 2m)} ] - [(3k)2 + (4r)2 +(- 2m)2 +{2 ×(3k)×(4r)} +{2 × (4r)×(- 2m)} +{2 ×(3k)×(-2m)} ]{ ∵(a + b +c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac }= [ 9k2 + 16r2 + 4m2+{ – 24kr} +{16rm } +{ – 12km } ] - [ 9k2 + 16r2 + 4m2 +{24kr } +{– 16rm } + { – 12km } ]= [ 9k2 + 16r2 + 4m2 – 24kr + 16rm – 12km ] - [ 9k2 + 16r2 + 4m2 + 24kr – 16rm – 12km ]= 9k2 + 16r2 + 4m2 – 24kr + 16rm – 12km – 9k2 – 16r2 – 4m2 – 24kr + 16rm + 12km

(3k – 4r – 2m)2 -(3k + 4r – 2m)2 = [(3k)2 +(- 4r)2 + (- 2m)2 +{2 ×(3k)×(- 4r)} +{2 ×(- 4r)× (-2m)} +{2 ×(3k)×(- 2m)} ] - [(3k)2 + (4r)2 +(- 2m)2 +{2 ×(3k)×(4r)} +{2 × (4r)×(- 2m)} +{2 ×(3k)×(-2m)} ]{ ∵(a + b +c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac }= [ 9k2 + 16r2 + 4m2+{ – 24kr} +{16rm } +{ – 12km } ] - [ 9k2 + 16r2 + 4m2 +{24kr } +{– 16rm } + { – 12km } ]= [ 9k2 + 16r2 + 4m2 – 24kr + 16rm – 12km ] - [ 9k2 + 16r2 + 4m2 + 24kr – 16rm – 12km ]= 9k2 + 16r2 + 4m2 – 24kr + 16rm – 12km – 9k2 – 16r2 – 4m2 – 24kr + 16rm + 12km= - 48kr + 32rm

(3k – 4r – 2m)2 -(3k + 4r – 2m)2 = [(3k)2 +(- 4r)2 + (- 2m)2 +{2 ×(3k)×(- 4r)} +{2 ×(- 4r)× (-2m)} +{2 ×(3k)×(- 2m)} ] - [(3k)2 + (4r)2 +(- 2m)2 +{2 ×(3k)×(4r)} +{2 × (4r)×(- 2m)} +{2 ×(3k)×(-2m)} ]{ ∵(a + b +c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac }= [ 9k2 + 16r2 + 4m2+{ – 24kr} +{16rm } +{ – 12km } ] - [ 9k2 + 16r2 + 4m2 +{24kr } +{– 16rm } + { – 12km } ]= [ 9k2 + 16r2 + 4m2 – 24kr + 16rm – 12km ] - [ 9k2 + 16r2 + 4m2 + 24kr – 16rm – 12km ]= 9k2 + 16r2 + 4m2 – 24kr + 16rm – 12km – 9k2 – 16r2 – 4m2 – 24kr + 16rm + 12km= - 48kr + 32rm= 32rm – 48kr

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Answer 2

Answer:

SSC (English Medium) 8th Standard

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Sum

Simplify.

(3k − 4r − 2m)2 − (3k + 4r − 2m)2

SOLUTION

It is known that,

(a+b+c)2=a2+b2+c2+2ab+2bc+2ca

(3k−4r−2m)2−(3k+4r−2m)2

=(3k)2+(−4r)2+(−2m)2+2×3k×(−4r)+2×(−4r)×(−2m)+2×(−2m)×3k−{(3k)2+(4r)2+(−2m)2+2×3k×4r+2×4r×(−2m)+2×(−2m)×3k}

=9k2+16r2+4m2−24kr+16rm−12mk−9k2−16r2−4m2−24kr+16rm+12mk

=32rm−48kr