x^2+2xy+2y-1factorize
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Solution:
x²+2xy+2y-1
= x²+2xy+y²-y²+2y-1
= (x²+2xy+y²)-(y²-2y+1²)
= (x+y)² - (y-1)²
= [(x+y)+(y-1)][(x+y)-(y-1)]
= (x+y+y-1)(x+y-y+1)
= (x+2y-1)(x+1)
Therefore,
x²+2xy+2y-1 = (x+2y-1)(x+1)
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