Question

the cost of a notebook is Rs. 3a²-4ab+6b². how much would 5a²b²notebooks cost?

please give step by step answer​

Answer 1

Given : -

• The Cost of one notebook is

⠀⠀⠀(3a² -4ab + 6b²)⠀⠀⠀⠀⠀⠀⠀⠀

To Find :- ⠀⠀⠀⠀⠀

• Cost of 5a²b² notebooks⠀⠀⠀⠀⠀⠀⠀⠀⠀

Solution :- ⠀

We know that Formula for finding the cost of 5a²b² notebooks is :-⠀⠀

⠀⠀⠀$\boxed{\sf\red{5a²b² × (cost \: of \: one \: notebook)}}$⠀⠀⠀⠀⠀

On putting the values in the formula we get :

$\sf{⟹5a²b² \times ({3a}^{2} - 4ab + {6b}^{2} ) }$⠀

By Disturbing terms we get,

$\sf{⟹5a²b² \times {3a}^{2} + 5a²b² \times - 4ab +5a²b² \times {6b}^{2} }$

By Taking out the constants,

$\sf{⟹(5 \times 3) {a}^{2} {a}^{2} {b}^{2} + (5 \times-4) {a}^{2}a {b}^{2}b + (5 \times 6) {a}^{2} {b}^{2} {b}^{2}}$

By applying identity : $\sf{{x}^{a} {x}^{b}= {x}^{a + b}}$

$\sf{⟹15{a}^{2 + 2} {b}^{2} - 20{a}^{2 + 1} {b}^{2 + 1} + 30{a}^{2} {b}^{2 + 2} }$

By Adding the terms we get,

$\sf\pink{⟹15{a}^{4} {b}^{2} - 20{a}^{3} {b}^{3} + 30{a}^{2} {b}^{4} }$⠀

Hence, The Cost of 5a²b² notebooks is :

(15a⁴b² - 20a³b³ + 30a²b⁴)

Answer 2

Step-by-step explanation:

Given : -

The Cost of one notebook is

⠀⠀⠀(3a² -4ab + 6b²)⠀⠀⠀⠀⠀⠀⠀⠀

To Find :- ⠀⠀⠀⠀⠀

Cost of 5a²b² notebooks⠀⠀⠀⠀⠀⠀⠀⠀⠀

Solution :- ⠀

We know that Formula for finding the cost of 5a²b² notebooks is :-⠀⠀

⠀⠀⠀\boxed{\sf\red{5a²b² × (cost \: of \: one \: notebook)}}

5a²b²×(costofonenotebook)

⠀⠀⠀⠀⠀

On putting the values in the formula we get :

\sf{⟹5a²b² \times ({3a}^{2} - 4ab + {6b}^{2} ) }⟹5a²b²×(3a

2

−4ab+6b

2

) ⠀

By Disturbing terms we get,

\sf{⟹5a²b² \times {3a}^{2} + 5a²b² \times - 4ab +5a²b² \times {6b}^{2} }⟹5a²b²×3a

2

+5a²b²×−4ab+5a²b²×6b

2

By Taking out the constants,

\sf{⟹(5 \times 3) {a}^{2} {a}^{2} {b}^{2} + (5 \times-4) {a}^{2}a {b}^{2}b + (5 \times 6) {a}^{2} {b}^{2} {b}^{2}}⟹(5×3)a

2

a

2

b

2

+(5×−4)a

2

ab

2

b+(5×6)a

2

b

2

b

2

By applying identity : \sf{{x}^{a} {x}^{b}= {x}^{a + b}}x

a

x

b

=x

a+b

\sf{⟹15{a}^{2 + 2} {b}^{2} - 20{a}^{2 + 1} {b}^{2 + 1} + 30{a}^{2} {b}^{2 + 2} }⟹15a

2+2

b

2

−20a

2+1

b

2+1

+30a

2

b

2+2

By Adding the terms we get,

\sf\pink{⟹15{a}^{4} {b}^{2} - 20{a}^{3} {b}^{3} + 30{a}^{2} {b}^{4} }⟹15a

4

b

2

−20a

3

b

3

+30a

2

b

4

⠀

Hence, The Cost of 5a²b² notebooks is (15a⁴b² - 20a³b³ + 30a²b⁴)

hope it will help you mate