Question

1) (x+1)(x+2)(3x-1)(3x-4)+12
2) a(a-1)x²-x-a(a+1)
can anyone answer these?

Answer 1

Hi ,

1 ) ( x+1)(x+2)(3x-1)(3x-4)+12

= [(x+1)(3x-1)][(x+2)(3x-4)] + 12

= ( 3x² -x + 3x - 1 )(3x² - 4x + 6x - 8 ) + 12

= ( 3x² + 2x - 1 )( 3x² + 2x - 8 ) + 12

= ( 3x² + 2x - 1 )( 3x² + 2x - 1 - 7 ) + 12

Let ( 3x² + 2x - 1 ) = m

= m ( m - 7 ) + 12

= m² - 7m + 12

= m² - 4m - 3m + 12

= m( m - 4 ) - 3( m - 4 )

= ( m - 4 )(m - 3 )

now ,

= ( 3x² + 2x - 1 - 4 ) ( 3x² + 2x - 1 - 3 )

= ( 3x² + 2x - 5 )( 3x² + 2x - 4 )

= [ 3x² +5x - 3x - 5]( 3x² + 2x - 4 )

= [ x( 3x + 5 ) - 1( 3x + 5 )] ( 3x² + 2x - 4 )

= ( 3x + 5 )( x - 1 ) ( 3x² + 2x - 4 )

2 ) a(a - 1 )x² - x - a(a + 1 )

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

= ( a - 1 )x [ ax + a + 1 ] - a ( ax + a + 1 )

= ( ax + a + 1 ) [ ( a - 1 )x - a ]

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

I hope this helps you.

: )