What is factor 27x^3-y^3+9x^2y-3xy^2 ?

The solution to factor 27x^3-y^3+9x^2y-3xy^2 is (3x+y)^2(3x-y)

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factor 27x^3-y^3+9x^2y-3xy^2

factor

27 x^{3} - y^{3} + 9 x^{2} y - 3 x y^{2}

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

Solution steps

27 x^{3} - y^{3} + 9 x^{2} y - 3 x y^{2}

Group by common factors

= 27 x^{3} + 9 x^{2} y - 3 x y^{2} - y^{3}

= (27 x^{3} + 9 x^{2} y) + (- 3 x y^{2} - y^{3})

Factor out

9 x^{2}

from

27 x^{3} + 9 x^{2} y : 9 x^{2} (3 x + y)

Factor out

- y^{2}

from

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

= 9 x^{2} (3 x + y) - y^{2} (3 x + y)

Factor out common term

3 x + y

= (3 x + y) (9 x^{2} - y^{2})

Factor

9 x^{2} - y^{2} : (3 x + y) (3 x - y)

= (3 x + y) (3 x + y) (3 x - y)

Apply exponent rule:

aa = a^{2}

(3 x + y) (3 x + y) = (3 x + y)^{2}

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

q^{16} (\frac{( 1 - cos ( x ) )}{( 1 + cos ( x ) )})

x^{3} - 6 x^{2} - 6 x + 1

\frac{( ( x ^{- 3} \cdot x ^{5} ) \cdot ( 3 y ) ^{3} )}{( x ^{- 1} \cdot x ^{2} )}

64 - 125 y^{3} - 24 y + 300 y^{2}

0.91 \cdot v^{1} + 4

What is factor 27x^3-y^3+9x^2y-3xy^2 ?
The solution to factor 27x^3-y^3+9x^2y-3xy^2 is (3x+y)^2(3x-y)