What is factor x^{15}y^{12}z^6-343 ?

The solution to factor x^{15}y^{12}z^6-343 is (x^5y^4z^2-7)(x^{10}y^8z^4+7x^5y^4z^2+49)

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factor x^{15}y^{12}z^6-343

factor

x^{15} y^{12} z^{6} - 343

(x^{5} y^{4} z^{2} - 7) (x^{10} y^{8} z^{4} + 7 x^{5} y^{4} z^{2} + 49)

Solution steps

x^{15} y^{12} z^{6} - 343

Rewrite

x^{15} y^{12} z^{6}

(x^{5} y^{4} z^{2})^{3}

= (x^{5} y^{4} z^{2})^{3} - 343

Rewrite

343

7^{3}

= (x^{5} y^{4} z^{2})^{3} - 7^{3}

Apply Difference of Cubes Formula:

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

(x^{5} y^{4} z^{2})^{3} - 7^{3} = (x^{5} y^{4} z^{2} - 7) ((x^{5} y^{4} z^{2})^{2} + 7 x^{5} y^{4} z^{2} + 7^{2})

= (x^{5} y^{4} z^{2} - 7) ((x^{5} y^{4} z^{2})^{2} + 7 x^{5} y^{4} z^{2} + 7^{2})

Refine

= (x^{5} y^{4} z^{2} - 7) ((x^{5} y^{4} z^{2})^{2} + 7 x^{5} y^{4} z^{2} + 49)

Simplify

(x^{5} y^{4} z^{2} - 7) ((x^{5} y^{4} z^{2})^{2} + 7 x^{5} y^{4} z^{2} + 49) : (x^{5} y^{4} z^{2} - 7) (x^{10} y^{8} z^{4} + 7 x^{5} y^{4} z^{2} + 49)

= (x^{5} y^{4} z^{2} - 7) (x^{10} y^{8} z^{4} + 7 x^{5} y^{4} z^{2} + 49)

10 am + 2 bm + bn + 5 an

ln (e^{2} + e^{3})

5 x (3 x + 2) (4 (3 x + 2))

e^{2 t + 2 c}

6 a x - 3 a y - 8 x + 4 y

What is factor x^{15}y^{12}z^6-343 ?
The solution to factor x^{15}y^{12}z^6-343 is (x^5y^4z^2-7)(x^{10}y^8z^4+7x^5y^4z^2+49)