What is factor 27x^3-343y^3 ?

The solution to factor 27x^3-343y^3 is (3x-7y)(9x^2+21xy+49y^2)

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factor 27x^3-343y^3

factor

27 x^{3} - 343 y^{3}

(3 x - 7 y) (9 x^{2} + 21 x y + 49 y^{2})

Solution steps

27 x^{3} - 343 y^{3}

Apply exponent rules

= (3 x)^{3} - (7 y)^{3}

Apply Difference of Cubes Formula:

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

(3 x)^{3} - (7 y)^{3} = (3 x - 7 y) ((3 x)^{2} + 3 x \cdot 7 y + (7 y)^{2})

= (3 x - 7 y) ((3 x)^{2} + 3 x \cdot 7 y + (7 y)^{2})

Simplify

(3 x)^{2} + 3 x \cdot 7 y + (7 y)^{2} : 9 x^{2} + 21 x y + 49 y^{2}

= (3 x - 7 y) (9 x^{2} + 21 x y + 49 y^{2})

4 y^{2} - 2 y - 12

r^{3} + 8 b^{3}

\frac{x ^{2}}{y ^{2}}

x^{2} - 8 x + 20 = 4 x

\frac{8 n ^{4}}{36 n ^{2}}

What is factor 27x^3-343y^3 ?
The solution to factor 27x^3-343y^3 is (3x-7y)(9x^2+21xy+49y^2)