What is factor 4p^2+2q^2+p^2q^2+8 ?

The solution to factor 4p^2+2q^2+p^2q^2+8 is (q^2+4)(p^2+2)

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factor 4p^2+2q^2+p^2q^2+8

factor

4 p^{2} + 2 q^{2} + p^{2} q^{2} + 8

(q^{2} + 4) (p^{2} + 2)

Solution steps

4 p^{2} + 2 q^{2} + p^{2} q^{2} + 8

Group by common factors

= p^{2} q^{2} + 4 p^{2} + 2 q^{2} + 8

= (p^{2} q^{2} + 4 p^{2}) + (2 q^{2} + 8)

Factor out

p^{2}

from

p^{2} q^{2} + 4 p^{2} : p^{2} (q^{2} + 4)

Factor out

2

from

2 q^{2} + 8 : 2 (q^{2} + 4)

= p^{2} (q^{2} + 4) + 2 (q^{2} + 4)

Factor out common term

q^{2} + 4

= (q^{2} + 4) (p^{2} + 2)

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What is factor 4p^2+2q^2+p^2q^2+8 ?
The solution to factor 4p^2+2q^2+p^2q^2+8 is (q^2+4)(p^2+2)