Question

(3k-4r-2m)-(3k+4r-2m) :simplify

Answer 1

Solution:

The simplified form of the given expression is -8r

Explanation:

We have to simplify the expression $(3k-4r-2m)-(3k+4r-2m)$

In order to simplify it, we can distribute the negative sign over the parenthesis.

$3k-4r-2m-3k-4r+2m$

Now we group the like terms.

$3k-3k-4r-4r-2m+2m$

Now, we can combine the like terms. 3k will get cancelled with by -3k and -2m will get cancelled with 2m and we are left with

$-4r-4r\\=-8r$

Therefore, the simplified form of the given expression is -8r

Answer 2

Answer:

Let us expand the given expression:

(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)}]

By using the formula,

(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

∴ (3k – 4r – 2m)2 – (3k + 4r – 2m)2 = 32rm – 48kr