2xy + 4x + 8y + 16
= 2[xy + 2x + 4y + 8]
= 2[x(y + 2) + 4(y + 2)]
= 2(y + 2)(x + 4)
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2xy - 4x plus 8y - 16 equals x plus 4 in parentheses multiplied by 2y minus 4 in parentheses. So, the factors are ( x + 4) and ( 2y - 4) .
2(x - 1)(2x + y)
They are four terms of an algebraic expression that can't be simplified
4x + 16 + 1 = 4x + 17 which cannot be factorised.
4x2 - 4x + 2xy - 2y = 4x(x - 1) + 2y(x - 1) = (x - 1)(4x + 2y) = 2(x - 1)(2x + y)