X 1 x 2 3x 1 3x 4 12
Asked by admin @ in Math viewed by 381 People
1) (x+1)(x+2)(3x-1)(3x-4)+12 2) a(a-1)x²-x-a(a+1)can anyone answer these?
Answered by admin @
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.
: )
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