What is factor 64x^6-729 ?

The solution to factor 64x^6-729 is (2x+3)(2x-3)(4x^2+6x+9)(4x^2-6x+9)

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factor 64x^6-729

factor

64 x^{6} - 729

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

Solution steps

64 x^{6} - 729

Apply exponent rules

= (4 x^{2})^{3} - 9^{3}

Apply Difference of Cubes Formula:

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

(4 x^{2})^{3} - 9^{3} = (4 x^{2} - 9) (4^{2} x^{4} + 9 \cdot 4 x^{2} + 9^{2})

= (4 x^{2} - 9) (4^{2} x^{4} + 9 \cdot 4 x^{2} + 9^{2})

Factor

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

= (2 x + 3) (2 x - 3) (4^{2} x^{4} + 9 \cdot 4 x^{2} + 9^{2})

Simplify

(2 x + 3) (2 x - 3) (4^{2} x^{4} + 9 \cdot 4 x^{2} + 9^{2}) : (2 x + 3) (2 x - 3) (16 x^{4} + 36 x^{2} + 81)

= (2 x + 3) (2 x - 3) (16 x^{4} + 36 x^{2} + 81)

Factor

16 x^{4} + 36 x^{2} + 81 : (4 x^{2} + 6 x + 9) (4 x^{2} - 6 x + 9)

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

\frac{( 9 x ^{3} - 9 x )}{( - 18 x ^{3} + 18 x )}

lo g_{10} (a^{2}) b^{3} c^{5}

\frac{( b ^{\frac{1}{3}} )}{( b ^{- \frac{3}{2}} \cdot b ^{\frac{1}{2}} )}

\frac{4}{3} \cdot n^{5} - \frac{1}{3} \cdot n^{4} + \frac{2}{3} \cdot n^{3} - \frac{5}{3} \cdot n^{2}

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

What is factor 64x^6-729 ?
The solution to factor 64x^6-729 is (2x+3)(2x-3)(4x^2+6x+9)(4x^2-6x+9)