What is factor (2xy)^3+2x^2y^{-1} ?

The solution to factor (2xy)^3+2x^2y^{-1} is (2x^2(4xy^4+1))/y

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factor (2xy)^3+2x^2y^{-1}

factor

(2 x y)^{3} + 2 x^{2} y^{- 1}

\frac{2 x ^{2} ( 4 x y ^{4} + 1 )}{y}

Solution steps

(2 x y)^{3} + 2 x^{2} y^{- 1}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

= 2^{3} x^{3} y^{3} + 2^{1} x^{2} y^{- 1}

Apply exponent rule:

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

x^{3} = x^{2} x, y^{3} = y^{- 1} y^{4}

= 8 x^{2} x y^{- 1} y^{4} + 2 x^{2} y^{- 1}

Rewrite as

= 4 \cdot 2 y^{- 1} x^{2} x y^{4} + 1 \cdot 2 y^{- 1} x^{2}

Factor out common term

2 y^{- 1} x^{2}

= 2 y^{- 1} x^{2} (4 x y^{4} + 1)

Refine

= \frac{2 x ^{2} ( 4 x y ^{4} + 1 )}{y}

aa c - a d + b c - b d

x^{5} + 4 x^{3} - 3 x^{2} + 4 x - 3 x d x

(d y) \cdot 5 x

A L (O H) 3

5 x 2 - 5 x + 4

What is factor (2xy)^3+2x^2y^{-1} ?
The solution to factor (2xy)^3+2x^2y^{-1} is (2x^2(4xy^4+1))/y