What is factor p^6+40p^3q+400q^2 ?

The solution to factor p^6+40p^3q+400q^2 is (p^3+20q)^2

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factor p^6+40p^3q+400q^2

factor

p^{6} + 40 p^{3} q + 400 q^{2}

(p^{3} + 20 q)^{2}

Solution steps

p^{6} + 40 p^{3} q + 400 q^{2}

Break the expression into groups

= (p^{6} + 20 p^{3} q) + (20 p^{3} q + 400 q^{2})

Factor out

p^{3}

from

p^{6} + 20 p^{3} q : p^{3} (p^{3} + 20 q)

Factor out

20 q

from

20 p^{3} q + 400 q^{2} : 20 q (p^{3} + 20 q)

= p^{3} (p^{3} + 20 q) + 20 q (p^{3} + 20 q)

Factor out common term

p^{3} + 20 q

= (p^{3} + 20 q) (p^{3} + 20 q)

Apply exponent rule:

aa = a^{2}

(p^{3} + 20 q) (p^{3} + 20 q) = (p^{3} + 20 q)^{2}

= (p^{3} + 20 q)^{2}

m^{2} - 4 m = 140

x^{2} - 22 x + 40

- 4 = 6 x - 3 x^{2}

15 x - 2 = 10 x + 23

3 x - 5 < 19

What is factor p^6+40p^3q+400q^2 ?
The solution to factor p^6+40p^3q+400q^2 is (p^3+20q)^2