Find the value


$4 a^{2}+b^{2}+4 a b+8 a+4 b+4=?$

(a) $(2 a+b+2)^{2}$

(b) $(2 a-b+2)^{2}$

(c) $(a+2 b+2)^{2}$

(d) none of these



(a) $(2 a+b+2)^{2}$

$4 a^{2}+b^{2}+4 a b+8 a+4 b+4$

$=4 a^{2}+b^{2}+4+4 a b+4 b+8 a$

$=(2 a)^{2}+b^{2}+2^{2}+2 \times 2 a \times b+2 \times b \times 2+2 \times 2 a \times 2$

$=(2 a+b+2)^{2}$


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