What is factor a^5+32b^{10} ?

The solution to factor a^5+32b^{10} is (a+2b^2)(a^4-2a^3b^2+4a^2b^4-8ab^6+16b^8)

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factor a^5+32b^{10}

factor

a^{5} + 32 b^{10}

(a + 2 b^{2}) (a^{4} - 2 a^{3} b^{2} + 4 a^{2} b^{4} - 8 a b^{6} + 16 b^{8})

Solution steps

a^{5} + 32 b^{10}

Rewrite

32 b^{10}

(2 b^{2})^{5}

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

Apply factoring rule:

x^{n} + y^{n} = (x + y) (x^{n - 1} - x^{n - 2} y + \dots - x y^{n - 2} + y^{n - 1})

n is odd

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

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

Simplify

(a + 2 b^{2}) (a^{4} - a^{3} \cdot 2 b^{2} + a^{2} (2 b^{2})^{2} - a (2 b^{2})^{3} + (2 b^{2})^{4}) : (a + 2 b^{2}) (a^{4} - 2 a^{3} b^{2} + 4 a^{2} b^{4} - 8 a b^{6} + 16 b^{8})

= (a + 2 b^{2}) (a^{4} - 2 a^{3} b^{2} + 4 a^{2} b^{4} - 8 a b^{6} + 16 b^{8})

6 x + 81 - 9

\frac{1}{3} x^{2} - 27

ln (sec (x) + tan (x)) (sin (x))

- (50)

(x + 1)^{2} - 12 (x + 1) + 32

What is factor a^5+32b^{10} ?
The solution to factor a^5+32b^{10} is (a+2b^2)(a^4-2a^3b^2+4a^2b^4-8ab^6+16b^8)