What is factor 8a^3-125b^3 ?

The solution to factor 8a^3-125b^3 is (2a-5b)(4a^2+10ab+25b^2)

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factor 8a^3-125b^3

factor

8 a^{3} - 125 b^{3}

(2 a - 5 b) (4 a^{2} + 10 ab + 25 b^{2})

Solution steps

8 a^{3} - 125 b^{3}

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

(2 a)^{2} + 2 a \cdot 5 b + (5 b)^{2} : 4 a^{2} + 10 ab + 25 b^{2}

= (2 a - 5 b) (4 a^{2} + 10 ab + 25 b^{2})

23 + 42

- 12 x^{3} + (x + 2) \cdot (2 x - 1) = (- 2 x^{2} + 1) \cdot (6 x - 1) + 9

x^{3} + 12 x^{2} + 44 x + 48

3 (x - 1)^{2} - 14 = - 2

(7 + 8) (7 - 8)

What is factor 8a^3-125b^3 ?
The solution to factor 8a^3-125b^3 is (2a-5b)(4a^2+10ab+25b^2)