Question

Factorise x²/8-y²/18 using the identity a² - b² = (a + b) (a - b).​

Answer 1

Answer:

$\frac{x^2}{8} -\frac{y^2}{18} =\frac{1}{2} (\frac{9x+ 4y}{36} )(\frac{9x- 4y}{36} )$

Step-by-step explanation:

Identity a² - b² = (a + b) (a - b)

$\frac{x^2}{8} -\frac{y^2}{18}$

Take 1/2 common

​$\frac{x^2}{8} -\frac{y^2}{18}\\=\frac{1}{2} (\frac{x^2}{4} -\frac{y^2}{9})\\=\frac{1}{2}[(\frac{x}{4})^2 -(\frac{y}{9})^2]\\=\frac{1}{2} (\frac{x}{4} +\frac{y}{9} )(\frac{x}{4} -\frac{y}{9})\\=\frac{1}{2} (\frac{9x+ 4y}{36} )(\frac{9x- 4y}{36} )$

Answer 2

Step-by-step explanation:

= (a + b) (a - b)

\frac{x^2}{8} -\frac{y^2}{18}

8

x

2

−

18

y

2

Take 1/2 common

\begin{gathered}\frac{x^2}{8} -\frac{y^2}{18}\\=\frac{1}{2} (\frac{x^2}{4} -\frac{y^2}{9})\\=\frac{1}{2}[(\frac{x}{4})^2 -(\frac{y}{9})^2]\\=\frac{1}{2} (\frac{x}{4} +\frac{y}{9} )(\frac{x}{4} -\frac{y}{9})\\=\frac{1}{2} (\frac{9x+ 4y}{36} )(\frac{9x- 4y}{36} )\end{gathered}

8

x

2

−

18

y

2

=

2

1

(

4

x

2

−

9

y

2

)

=

2

1

[(

4

x

)

2

−(

9

y

)

2

]

=

2

1

(

4

x

+

9

y

)(

4

x

−

9

y

)

=

2

1

(

36

9x+4y

)(

36

9x−4y

).