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Factorise is it? Here are three ways :
a² + ab + 2a + b + 1
= a² + ab + a + a + b + 1
= a(a + b + 1) + a + b + 1
= (a + b + 1)(a + 1)
Or
a² + ab + 2a + b + 1
= a² + 2a + 1 + ab + b
= (a + 1)(a + 1) + b(a + 1)
= (a + 1)(a + 1 + b)
Or
a² + ab + 2a + b + 1
= a² + a + ab + b + a + 1
= a(a + 1) + b(a + 1) + a + 1
= (a + 1)(a + b + 1)
a² + ab + 2a + b + 1
= a² + ab + a + a + b + 1
= a(a + b + 1) + a + b + 1
= (a + b + 1)(a + 1)
Or
a² + ab + 2a + b + 1
= a² + 2a + 1 + ab + b
= (a + 1)(a + 1) + b(a + 1)
= (a + 1)(a + 1 + b)
Or
a² + ab + 2a + b + 1
= a² + a + ab + b + a + 1
= a(a + 1) + b(a + 1) + a + 1
= (a + 1)(a + b + 1)