What is factor 27x^3+125y^3 ?

The solution to factor 27x^3+125y^3 is (3x+5y)(9x^2-15xy+25y^2)

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factor 27x^3+125y^3

factor

27 x^{3} + 125 y^{3}

(3 x + 5 y) (9 x^{2} - 15 x y + 25 y^{2})

Solution steps

27 x^{3} + 125 y^{3}

Apply exponent rules

= (3 x)^{3} + (5 y)^{3}

Apply Sum of Cubes Formula:

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

(3 x)^{3} + (5 y)^{3} = (3 x + 5 y) ((3 x)^{2} - 3 x \cdot 5 y + (5 y)^{2})

= (3 x + 5 y) ((3 x)^{2} - 3 x \cdot 5 y + (5 y)^{2})

Simplify

(3 x)^{2} - 3 x \cdot 5 y + (5 y)^{2} : 9 x^{2} - 15 x y + 25 y^{2}

= (3 x + 5 y) (9 x^{2} - 15 x y + 25 y^{2})

∣ x ∣ > 15

1 - 4 b + 4 b^{2}

4 (- \frac{1}{2})^{2} - 20 (- \frac{1}{2}) + 25

14 + \frac{12}{- 4}

(x - 3) (x - 1) \leq 0

What is factor 27x^3+125y^3 ?
The solution to factor 27x^3+125y^3 is (3x+5y)(9x^2-15xy+25y^2)