Question

A shirt costs (a^2-ab-b^2), a pair of trousers costs (2a^2+8ab-2b^2), and a pair of shoes costs (a^2-3ab+4b^2). After collecting these three items from the store, Ranjan paid (2a+b)^2. What balance will ranjan receive from the cashier?

Answer 1

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Answer 2

Step-by-step explanation:

Given: The cost of the shirt is $(a^{2} -ab-b^{2} )$, cost of pair of trousers is $(2a^{2} +8ab-2b^{2} )$ and the cost of pair of shoes is $(a^{2} -3ab + 4b^{2} )$. Ranjan has paid $(2a+b)^{2}$.

To find: Balance Ranjan will receive from the cashier.

For calculating the balance Ranjan will receive,

i. We know that cost of the shirt is $(a^{2} -ab-b^{2} )$, cost of pair of trousers is $(2a^{2} +8ab-2b^{2} )$ and cost of pair of shoes is $(a^{2} -3ab + 4b^{2} )$

⇒ The total cost = $(a^{2} -ab-b^{2} ) +$ $(2a^{2} +8ab-2b^{2} ) +$ $(a^{2} -3ab + 4b^{2} )$

⇒ $a^{2} - ab - b^{2} + 2a^{2} + 8ab - 2b^{2} + a^{2} - 3ab + 4b^{2}$

⇒ $2a^{2} + 4ab + b^{2}$

ii. The total money Ranjan paid,

⇒ $(2a+b)^{2}$

⇒ $2a^{2} + b^{2} + 4ab$

⇒ $4a^{2} + b^{2} + 4ab$

iii. The balance of money Ranjan will receive is,

⇒ $(2a^{2} + 4ab + b^{2}) -$ $(4a^{2} + b^{2} + 4ab)$

⇒ $2a^{2} + 4ab + b^{2} - 4a^{2} - b^{2} - 4ab$

⇒ $4a^{2} -2a^{2}$ $= 2a^{2}$

Ranjan will receive a balance of Rs. $2a^{2}$.