Math, asked by gouri61, 1 year ago

Factorise (x2+4)−2a−a2−5.​

Answers

Answered by praneethks
17

Step-by-step explanation:

 ({x}^{2} + 4) - 2a -  {a}^{2}  - 5 =  >  {x}^{2} -

2a -  {a}^{2} - 1 =  >  {x}^{2} - ( {a}^{2} + 2a + 1)

 =  >  {x}^{2} -  {(a + 1)}^{2} =  >

(x - (a + 1))(x + (a + 1))

Hope it helps you.

Answered by pulakmath007
3

( x² + 4 ) - 2a - a² - 5 = (x + a + 1)(x - a - 1)

Given :

The expression ( x² + 4 ) - 2a - a² - 5

To find :

To factorise the expression

Formula :

  • (a + b)² = a² + 2ab + b²

  • a² - b² = ( a + b ) ( a - b )

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

( x² + 4 ) - 2a - a² - 5

Step 2 of 2 :

Factorise the expression

 \sf ( {x}^{2}  + 4) - 2a -  {a}^{2}  - 5

 \sf  =  {x}^{2}  + 4 - 2a -  {a}^{2}  - 5

 \sf  =  {x}^{2}   - 2a -  {a}^{2}  - 1

 \sf  =  {x}^{2}    -  ({a}^{2}  + 2a + 1)

 \sf  =  {x}^{2}    -  ({a}^{2}  + 2.a .1+  {1}^{2} )

 \sf  =  {x}^{2}    -  {(a + 1)} ^{2}   \:   \:  \bigg[\:  \because \:  {a}^{2}  + 2ab +  {b}^{2}  =  {(a + b)}^{2}  \bigg]

 \sf  = (x + a + 1)(x - a - 1)\:   \:  \bigg[\:  \because \:  {a}^{2}   -   {b}^{2}  = (a + b)(a  -  b)  \bigg]

∴ ( x² + 4 ) - 2a - a² - 5 = (x + a + 1)(x - a - 1)

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