What is factor 27r^3-8 ?

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

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factor 27r^3-8

factor

27 r^{3} - 8

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

Solution steps

27 r^{3} - 8

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

\frac{y ^{2} + 2 y - 3}{y ^{2} - 3 y - 18} \cdot \frac{4 y ^{2} - 24 y}{2 y ^{2} - 2 y}

\frac{29}{6}

(7 - 8 i) + (- 12 - 4 i)

(2 x^{3} + 5 x - 3) + (2 x^{3} - 3 x^{2} + 4 x)

\frac{42 x ^{9} y ^{2}}{- 7 x ^{5} y ^{2}}