1,
20x7 + 7x - 6
= 20x7 - 8x + 15x - 6
= (20x7 - 8x )+ (15x - 6)
= 4x( 5x - 2 ) + 3( 5x - 2)
= ( 5x - 2 )( 4x + 3 )
2/
x4 - 5x2y2 + 4y4
= x4 - 4x2y2 - x2y2 + 4y2
= (x4 - 4x2y2 + 4y2) - x2y2
= ( x2 - 2y2)2 - x2y2
= ( x2 - 2y2)2 - (xy)2
= ( x2 - 2y2 - xy)( x2 - 2y2 + xy)
3/
x8 + y4 + 1
= ( x8 - x2 ) + ( x4 + 1 + x2 )
= x2( x6 - 1) + ( x4 + 1 + x2 )
= x2( x3 - 1 )( x3 + 1) + ( x4 + 1 + x2 )
= x2 . ( x - 1 ).( x2 + x + 1 ). ( x - 1).(x2 - x + 1) + ( x4 + 1 + x2 )
= x2 . \(\left[\left(x-1\right)\left(x+1\right)\right].\)\(\left[\left(x^2+x+1\right)\left(x^2-x+1\right)\right]\)+ ( x4 + 1 + x2 )
= x2(x2 - 1 )\(\left[\left(x^2+1\right)^2-x^2\right]\)+ ( x4 + 1 + x2 )
= x2(x2 - 1 )( x4 + 2x2 + 1 - x2 ) + ( x4 + 1 + x2 )
= x2(x2 - 1 )( x4 +x2 + 1 ) + ( x4 + 1 + x2 )
= ( x4 - x2 )( x4 +x2 + 1 ) + ( x4 + 1 + x2 )
= ( x4 +x2 + 1 )( x4 - x2 + 1 )
