4x^3-16x^2y+16xy^2
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4x^3-16x^2y+16xy^2
(x²-2y)²-(1-2y)²
x^4-8x²y²+16y^4
(x²-2y)²-(1-2y)²
x^4-8x²y²+16y^4
4x^3-16x^2y+16xy^2
=4x(x^2-4xy+4y^2)
=4x[x^2-2*x*2y+(2y)^2]
=4x(x-2y)^2
(x²-2y)²-(1-2y)²
=[(x^2-2y)+(1-2y)][(x^2-2y)-(1-2y)]
=(x^2-2y+1-2y)(x^2-2y-1+2y)
=(x^2-4y+1)(x^2-1)
=(x^2-4y+1)(x+1)(x-1)
x^4-8x²y²+16y^4
=(x^2)^2-2*(x^2)*(4y^2)+(4y^2)^2
=(x^2-4y^2)^2
=(x+2y)^2(x-2y)^2
=4x(x^2-4xy+4y^2)
=4x[x^2-2*x*2y+(2y)^2]
=4x(x-2y)^2
(x²-2y)²-(1-2y)²
=[(x^2-2y)+(1-2y)][(x^2-2y)-(1-2y)]
=(x^2-2y+1-2y)(x^2-2y-1+2y)
=(x^2-4y+1)(x^2-1)
=(x^2-4y+1)(x+1)(x-1)
x^4-8x²y²+16y^4
=(x^2)^2-2*(x^2)*(4y^2)+(4y^2)^2
=(x^2-4y^2)^2
=(x+2y)^2(x-2y)^2
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