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

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

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factor 27p^3-8q^3

factor

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

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

Solution steps

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

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

f (x) = \frac{x ^{2} - 4}{x ^{2} - x - 6}

3 (2 x + 1) (4 x + 1)

x^{2} + 5 x - 25 y - 5 x y

5 \cdot (- 6)

f (n) = \frac{3 + n - 2 n ^{2}}{1 + n}

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