What is factor 1000x^3y^6+343z^3 ?

The solution to factor 1000x^3y^6+343z^3 is (10xy^2+7z)(100x^2y^4-70xy^2z+49z^2)

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factor 1000x^3y^6+343z^3

factor

1000 x^{3} y^{6} + 343 z^{3}

(10 x y^{2} + 7 z) (100 x^{2} y^{4} - 70 x y^{2} z + 49 z^{2})

Solution steps

1000 x^{3} y^{6} + 343 z^{3}

Rewrite

1000 x^{3} y^{6}

(10 x y^{2})^{3}

Rewrite

343 z^{3}

(7 z)^{3}

= (10 x y^{2})^{3} + (7 z)^{3}

Apply Sum of Cubes Formula:

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

(10 x y^{2})^{3} + (7 z)^{3} = (10 x y^{2} + 7 z) ((10 x y^{2})^{2} - 7 z 10 x y^{2} + (7 z)^{2})

= (7 z + 10 x y^{2}) ((7 z)^{2} - 7 z 10 x y^{2} + (10 x y^{2})^{2})

Simplify

(10 x y^{2} + 7 z) ((10 x y^{2})^{2} - 7 z \cdot 10 x y^{2} + (7 z)^{2}) : (10 x y^{2} + 7 z) (100 x^{2} y^{4} - 70 x y^{2} z + 49 z^{2})

= (10 x y^{2} + 7 z) (100 x^{2} y^{4} - 70 x y^{2} z + 49 z^{2})

3 ab + 12 a d - 8 c d - 2 b c

- 216 - x^{3}

x^{2} + 4 x y + x (\frac{d y}{d x})

1 - 0.25 cos^{2} (10 t)

\frac{4 + 72}{4}

What is factor 1000x^3y^6+343z^3 ?
The solution to factor 1000x^3y^6+343z^3 is (10xy^2+7z)(100x^2y^4-70xy^2z+49z^2)