Question

Resolve into factors :--

a(a-1) x² + (2a²-1)x + a(a+1)​

Answer 1

Answer:

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

Step-by-step explanation:

Given---->

a ( a - 1 )x² + ( 2a² - 1 ) x + a ( a + 1 )

To find----> Resolve in to factors

Solution----> ATQ,

a ( a - 1 )x² + ( 2a² - 1 )x + a ( a +1 )

We break ,

2a² - 1 = ( a² + a² ) - 1

Rearranging terms , we get,

= ( a² - 1 ) + a²

= { ( a )² - ( 1 )² } + a²

Applying a² - b² = ( a + b ) ( a - b ) , we get ,

= ( a + 1 ) ( a - 1 ) + a²

Now returning to original problem

a( a - 1 )x² + ( 2a² - 1 ) x + a ( a + 1 )

Now putting value of ( 2a² - 1 ) , we get,

a( a - 1 )x² + { ( a + 1 ) ( a - 1 ) + a² } x + a ( a + 1 )

Multiplying by x in middle term , we get,

=> a ( a - 1 )x² + ( a + 1 ) ( a - 1 ) x + a²x + a ( a + 1 )

Taking ( a - 1 )x , Common from first two terms and taking a , common from last two terms

=> ( a - 1 )x { ax + ( a + 1 ) } + a { ax + ( a + 1 ) }

Taking { ax + ( a + 1 ) } common , we get,

=> { ax + ( a + 1 ) } { ( a - 1 )x + a }

=> ( ax + a + 1 ) ( ax - x + a )