a) x4 - 4x2 + 4x - 1
= ( x2)2 - [ ( 2x)2 - 2.2x + 1]
= ( x2)2 - ( 2x - 1)2
= ( x2 - 2x +1)( x2 + 2x - 1)
= ( x -1)2( x2 + 2x - 1)
b) 4x2 - y2 + 4x + 1
= (2x)2 + 2.2x +1 - y2
= ( 2x +1)2 - y2
= ( 2x + 1 - y)( 2x + 1 + y)
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\(\text{a) }x^4-4x^2+4x-1\\ \\=x^4-\left(4x^2-4x+1\right)\\ \\ =\left(x^2\right)^2-\left(2x-1\right)^2\\ \\=\left(x^2-2x+1\right)\left(x^2+2x-1\right)\\ \\=\left(x-1\right)^2\left(x^2+2x-1\right)\)
\(\text{b) }4x^2-y^2+4x+1\\ \\=\left(4x^2+4x+1\right)-y^2\\ \\=\left(2x+1\right)^2-y^2\\ \\=\left(2x+1+y\right)\left(2x+1-y\right)\)
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