What is factor 8p^3-27q^3r^3 ?

The solution to factor 8p^3-27q^3r^3 is (2p-3qr)(4p^2+6pqr+9q^2r^2)

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factor 8p^3-27q^3r^3

factor

8 p^{3} - 27 q^{3} r^{3}

(2 p - 3 q r) (4 p^{2} + 6 pq r + 9 q^{2} r^{2})

Solution steps

8 p^{3} - 27 q^{3} r^{3}

Rewrite

8 p^{3}

(2 p)^{3}

Rewrite

27 q^{3} r^{3}

(3 q r)^{3}

= (2 p)^{3} - (3 q r)^{3}

Apply Difference of Cubes Formula:

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

(2 p)^{3} - (3 q r)^{3} = (2 p - 3 q r) ((2 p)^{2} + 3 q r 2 p + (3 q r)^{2})

= (2 p - 3 q r) ((3 q r)^{2} + 3 q r 2 p + (2 p)^{2})

Simplify

(2 p - 3 q r) ((2 p)^{2} + 3 q r \cdot 2 p + (3 q r)^{2}) : (2 p - 3 q r) (4 p^{2} + 6 pq r + 9 q^{2} r^{2})

= (2 p - 3 q r) (4 p^{2} + 6 pq r + 9 q^{2} r^{2})

sin (2 x^{2} y + 4 y^{2})

3 x^{2} - 5 x - 9 x - 15

x y + 2 m x - m y - 2 m^{2}

10 6 + 26

What is factor 8p^3-27q^3r^3 ?
The solution to factor 8p^3-27q^3r^3 is (2p-3qr)(4p^2+6pqr+9q^2r^2)