What is factor 125a^9b^3+64s^6g^6 ?

The solution to factor 125a^9b^3+64s^6g^6 is (5a^3b+4s^2g^2)(25a^6b^2-20a^3bs^2g^2+16s^4g^4)

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factor 125a^9b^3+64s^6g^6

factor

125 a^{9} b^{3} + 64 s^{6} g^{6}

(5 a^{3} b + 4 s^{2} g^{2}) (25 a^{6} b^{2} - 20 a^{3} b s^{2} g^{2} + 16 s^{4} g^{4})

Solution steps

125 a^{9} b^{3} + 64 s^{6} g^{6}

Rewrite

125 a^{9} b^{3}

(5 a^{3} b)^{3}

Rewrite

64 s^{6} g^{6}

(2 s g)^{6}

= (5 a^{3} b)^{3} + (2 s g)^{6}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

(2 s g)^{6} = ((2 s g)^{2})^{3}

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

Apply Sum of Cubes Formula:

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

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

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

Simplify

(5 a^{3} b + (2 s g)^{2}) ((5 a^{3} b)^{2} - 5 a^{3} b (2 s g)^{2} + (2 s g)^{4}) : (5 a^{3} b + 4 s^{2} g^{2}) (25 a^{6} b^{2} - 20 a^{3} b s^{2} g^{2} + 16 s^{4} g^{4})

= (5 a^{3} b + 4 s^{2} g^{2}) (25 a^{6} b^{2} - 20 a^{3} b s^{2} g^{2} + 16 s^{4} g^{4})

1000 + 6 %^{6}

[cos (a) sinh (a)]

(3) - x + 3 y

(6.8) θ

- cos (2 x - 90)

What is factor 125a^9b^3+64s^6g^6 ?
The solution to factor 125a^9b^3+64s^6g^6 is (5a^3b+4s^2g^2)(25a^6b^2-20a^3bs^2g^2+16s^4g^4)