What is factor p^3q^3-343r^3s^3 ?

The solution to factor p^3q^3-343r^3s^3 is (pq-7rs)(p^2q^2+7pqrs+49r^2s^2)

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factor p^3q^3-343r^3s^3

factor

p^{3} q^{3} - 343 r^{3} s^{3}

(pq - 7 rs) (p^{2} q^{2} + 7 pq rs + 49 r^{2} s^{2})

Solution steps

p^{3} q^{3} - 343 r^{3} s^{3}

Rewrite

p^{3} q^{3}

(pq)^{3}

Rewrite

343 r^{3} s^{3}

(7 rs)^{3}

= (pq)^{3} - (7 rs)^{3}

Apply Difference of Cubes Formula:

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

(pq)^{3} - (7 rs)^{3} = (pq - 7 rs) ((pq)^{2} + pq 7 rs + (7 rs)^{2})

= (pq - 7 rs) ((pq)^{2} + pq 7 rs + (7 rs)^{2})

Simplify

(pq - 7 rs) ((pq)^{2} + pq \cdot 7 rs + (7 rs)^{2}) : (pq - 7 rs) (p^{2} q^{2} + 7 pq rs + 49 r^{2} s^{2})

= (pq - 7 rs) (p^{2} q^{2} + 7 pq rs + 49 r^{2} s^{2})

sin^{2} (x) + 5 sin (x) + 6

3 y 6

2 (\frac{1}{2} x^{2} - 2)

- \infty - (\infty)

(3 x + 1)^{2} + 13 (3 x + 1) + 36

What is factor p^3q^3-343r^3s^3 ?
The solution to factor p^3q^3-343r^3s^3 is (pq-7rs)(p^2q^2+7pqrs+49r^2s^2)