What is factor 27a^3-343b^3 ?

The solution to factor 27a^3-343b^3 is (3a-7b)(9a^2+21ab+49b^2)

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factor 27a^3-343b^3

factor

27 a^{3} - 343 b^{3}

(3 a - 7 b) (9 a^{2} + 21 ab + 49 b^{2})

Solution steps

27 a^{3} - 343 b^{3}

Apply exponent rules

= (3 a)^{3} - (7 b)^{3}

Apply Difference of Cubes Formula:

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

(3 a)^{3} - (7 b)^{3} = (3 a - 7 b) ((3 a)^{2} + 3 a \cdot 7 b + (7 b)^{2})

= (3 a - 7 b) ((3 a)^{2} + 3 a \cdot 7 b + (7 b)^{2})

Simplify

(3 a)^{2} + 3 a \cdot 7 b + (7 b)^{2} : 9 a^{2} + 21 ab + 49 b^{2}

= (3 a - 7 b) (9 a^{2} + 21 ab + 49 b^{2})

2 a (x + 2) + a^{2} (- x - 2)

7^{2} x + 3 - 4 9^{x} + \frac{2}{34 3 ^{n + 1}} \frac{2}{3}

(13 + y)^{3}

\frac{( 1 + x + x ^{2} + x ^{3} )}{( 1 + x )}

(2 cos^{2} (x) - 1)^{2}

What is factor 27a^3-343b^3 ?
The solution to factor 27a^3-343b^3 is (3a-7b)(9a^2+21ab+49b^2)