Question

*If the cost of one pen is (a² + 10a + 25) then find the total cost of (a+5) numbers of such pens?*

1️⃣ ₹(a³ +15a²+75a+125)
2️⃣ ₹(a³ +25a²+25a+125)
3️⃣ ₹(a³ -15a²+75a - 125)
4️⃣ ₹(a² +25a+75)​

Answer 1

Given :- If the cost of one pen is (a² + 10a + 25) then find the total cost of (a+5) numbers of such pens?*

1️⃣ ₹(a³ +15a²+75a+125)

2️⃣ ₹(a³ +25a²+25a+125)

3️⃣ ₹(a³ -15a²+75a - 125)

4️⃣ ₹(a² +25a+75)

Answer :-

we have,

→ Cost of 1 pen = (a² + 10a + 25)

→ cost of (a + 5) pens = 1 pen cost * (a + 5)

solving,

→ (a + 5)(a² + 10a + 25)

→ (a + 5){(a)² + 2*5*a + (5)²}

→ (a + 5)(a + 5)²

→ (a + 5)³

using :-

• (a + b)³ = a³ + b³ + 3ab² + 3a²b

→ a³ + 125 + 3*a*25 + 3a²5

→ (a³ + 15a² + 75a + 125) (Option 1) (Ans.)

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

If the cost of one pen is (a² + 10a + 25) then find the total cost of (a+5) numbers of such pens

1. ₹ (a³ +15a²+75a+125)

2. ₹ (a³ +25a²+25a+125)

3. ₹ (a³ -15a²+75a - 125)

4. ₹ (a² +25a+75)

EVALUATION

Here it is given that the cost of one pen is

₹ (a² + 10a + 25)

Now we have to find the total cost of (a+5) numbers of such pens

So number of quantity = a + 5

Hence the required total cost

$\sf{ = Number \: of \: quantity \times Cost \: per \: quantity }$

$\sf{ = (a + 5) \times ( {a}^{2} + 10a + 25) }$

$\sf{ = a \times ( {a}^{2} + 10a + 25)+ 5 \times ( {a}^{2} + 10a + 25) \: \:( by \: distributive \: property) }$

$\sf{ = {a}^{3} + 10 {a}^{2} + 25a+ 5 {a}^{2} + 50a + 125}$

$\sf{ = {a}^{3} + 15{a}^{2} +75a+ 125}$

FINAL ANSWER

Hence the correct option is

1. ₹ ( a³ + 15a² + 75a + 125 )

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