What is factor R^{18}+512 ?

The solution to factor R^{18}+512 is (R^2+2)(R^4-2R^2+4)(R^{12}-8R^6+64)

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factor R^{18}+512

factor

R^{18} + 512

(R^{2} + 2) (R^{4} - 2 R^{2} + 4) (R^{12} - 8 R^{6} + 64)

Solution steps

R^{18} + 512

Apply exponent rules

= (R^{6})^{3} + 8^{3}

Apply Sum of Cubes Formula:

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

(R^{6})^{3} + 8^{3} = (R^{6} + 8) (R^{12} - 8 R^{6} + 8^{2})

= (R^{6} + 8) (R^{12} - 8 R^{6} + 8^{2})

Factor

R^{6} + 8 : (R^{2} + 2) (R^{4} - 2 R^{2} + 2^{2})

= (R^{2} + 2) (R^{4} - 2 R^{2} + 2^{2}) (R^{12} - 8 R^{6} + 8^{2})

Simplify

(R^{2} + 2) (R^{4} - 2 R^{2} + 2^{2}) (R^{12} - 8 R^{6} + 8^{2}) : (R^{2} + 2) (R^{4} - 2 R^{2} + 4) (R^{12} - 8 R^{6} + 64)

= (R^{2} + 2) (R^{4} - 2 R^{2} + 4) (R^{12} - 8 R^{6} + 64)

(- 7.5) (7.3)

(x + 6) (x - 6) - (x - 6)^{2}

511 \times 22 \times 22

50 \cdot \frac{π}{180}

2 x - \frac{2}{x ^{2}}

What is factor R^{18}+512 ?
The solution to factor R^{18}+512 is (R^2+2)(R^4-2R^2+4)(R^{12}-8R^6+64)