(a+b+2)(a+b) - (a-b)^2 + 1 = a^2+ab+2a+ab+b^2+2b-a^2+2ab-b^2+1 =
= (a^2-a^2) + (b^2-b^2) + 4ab + 2a + 2b + 1 = 4ab + 2a + 2b + 1 =
= 2a(2b + 1) + (2b + 1) = (2a+1)(2b+1)
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(a+b+2)(a+b) - (a-b)^2 + 1 = a^2+ab+2a+ab+b^2+2b-a^2+2ab-b^2+1 =
= (a^2-a^2) + (b^2-b^2) + 4ab + 2a + 2b + 1 = 4ab + 2a + 2b + 1 =
= 2a(2b + 1) + (2b + 1) = (2a+1)(2b+1)