Question

Simplify : (1/5x + 2y) x (2/3x - y)​

Answer 1

Answer:

(

5

1

x+2y)(

3

2

x−y)

=(

5

1

x+

1×5

2×5

y)(

3

2

x−

1×3

1×3

y)(TakingLCM)

=(

5

1

x+

5

10

y)(

3

2

x−

3

3

y)

=(

5

x+10y

)(

3

2x−3y

)

=

15

1

(x+10y)(2x−3y)

=

15

1

(2x

2

−3xy+20xy−30y

2

)

=

15

2x

2

−30y

2

+17xy

Hence, (

5

1

x+2y)(

3

2

x−y)=

15

2x

2

−30y

2

+17xy

Answer 2

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$\underline{\textbf{\textsf{\orange{Solution:}}}}$

Simplify :

$\: \bullet \bf{ \bigg( \frac{1}{5}x + 2y \bigg) \times \bigg( \frac{2}{3} x - y \bigg)}$

$\: \implies \displaystyle \sf{ \bigg( \frac{x}{5} + 2y \bigg) \bigg( \frac{2x}{3} - y \bigg)}$

$\: \\ \implies \displaystyle \sf{ \bigg( \frac{x}{5} \bigg( \frac{2x}{3} - y \bigg) + 2y \bigg (\frac{2x}{3} - y \bigg)} \bigg)$

$\: \implies \displaystyle \sf \bigg( \frac{2 {x}^{2} }{15} - \frac{xy}{5} + \frac{4xy}{3} - 2 {y}^{2} \bigg)$

$\: \\ \implies \displaystyle \sf \: \bigg( \frac{2 {x}^{2} }{15} - \frac{3xy + 20xy}{15} - 2 {y}^{2} \bigg)$

$\: \implies \displaystyle \sf \bigg( \frac{2 {x}^{2} }{15} + \frac{ 17xy}{15} - 2 {y}^{2} \bigg)$

$\: \implies \displaystyle \sf \: \bigg( 2 {x}^{2} + 17xy - 30 {y}^{2} \bigg)$