What is factor a^6+125b^{12} ?

The solution to factor a^6+125b^{12} is (a^2+5b^4)(a^4-5a^2b^4+25b^8)

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factor a^6+125b^{12}

factor

a^{6} + 125 b^{12}

(a^{2} + 5 b^{4}) (a^{4} - 5 a^{2} b^{4} + 25 b^{8})

Solution steps

a^{6} + 125 b^{12}

Apply exponent rules

= (a^{2})^{3} + (5 b^{4})^{3}

Apply Sum of Cubes Formula:

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

(a^{2})^{3} + (5 b^{4})^{3} = (a^{2} + 5 b^{4}) ((a^{2})^{2} - a^{2} \cdot 5 b^{4} + (5 b^{4})^{2})

= (a^{2} + 5 b^{4}) ((a^{2})^{2} - a^{2} \cdot 5 b^{4} + (5 b^{4})^{2})

Simplify

(a^{2})^{2} - a^{2} \cdot 5 b^{4} + (5 b^{4})^{2} : a^{4} - 5 a^{2} b^{4} + 25 b^{8}

= (a^{2} + 5 b^{4}) (a^{4} - 5 a^{2} b^{4} + 25 b^{8})

6^{- x}

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

e^{0} + e^{- 0}

\frac{6}{72}

\frac{( 8 ^{2022} )}{4}

What is factor a^6+125b^{12} ?
The solution to factor a^6+125b^{12} is (a^2+5b^4)(a^4-5a^2b^4+25b^8)