What is factor 6(2p+q)^2+(2p+q)^{-2} ?

The solution to factor 6(2p+q)^2+(2p+q)^{-2} is (6(q+2p)^4+1)/((q+2p)^2)

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factor 6(2p+q)^2+(2p+q)^{-2}

factor

6 (2 p + q)^{2} + (2 p + q)^{- 2}

\frac{6 ( q + 2 p ) ^{4} + 1}{( q + 2 p ) ^{2}}

Solution steps

6 (2 p + q)^{2} + (2 p + q)^{- 2}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

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

= 6 (q + 2 p)^{- 2} (q + 2 p)^{4} + (q + 2 p)^{- 2}

Factor out common term

(q + 2 p)^{- 2}

= (q + 2 p)^{- 2} (6 (q + 2 p)^{4} + 1)

Refine

= \frac{6 ( 2 p + q ) ^{4} + 1}{( 2 p + q ) ^{2}}

x e^{2} + 2 x

27 y^{3} - 8 y^{3}

1 + (- x)

- 2 x^{5} + 4

x^{2} - 11 + 24

What is factor 6(2p+q)^2+(2p+q)^{-2} ?
The solution to factor 6(2p+q)^2+(2p+q)^{-2} is (6(q+2p)^4+1)/((q+2p)^2)