What is ((24x^8y^6z^4-64x^5y^4z^3+40x^3y^4z^5))/((-8x^3y^4z^2)) ?

The solution to ((24x^8y^6z^4-64x^5y^4z^3+40x^3y^4z^5))/((-8x^3y^4z^2)) is -z(3x^5y^2z-8x^2+5z^2)

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simplify ((24x^8y^6z^4-64x^5y^4z^3+40x^3y^4z^5))/((-8x^3y^4z^2))

simplify

\frac{( 24 x ^{8} y ^{6} z ^{4} - 64 x ^{5} y ^{4} z ^{3} + 40 x ^{3} y ^{4} z ^{5} )}{( - 8 x ^{3} y ^{4} z ^{2} )}

- z (3 x^{5} y^{2} z - 8 x^{2} + 5 z^{2})

Solution steps

\frac{24 x ^{8} y ^{6} z ^{4} - 64 x ^{5} y ^{4} z ^{3} + 40 x ^{3} y ^{4} z ^{5}}{- 8 x ^{3} y ^{4} z ^{2}}

Factor out common term

8 x^{3} y^{4} z^{3} : 8 x^{3} y^{4} z^{3} (3 x^{5} y^{2} z - 8 x^{2} + 5 z^{2})

= \frac{8 x ^{3} y ^{4} z ^{3} ( 3 x ^{5} y ^{2} z - 8 x ^{2} + 5 z ^{2} )}{- 8 x ^{3} y ^{4} z ^{2}}

Cancel the common factor:

8

= \frac{x ^{3} y ^{4} z ^{3} ( 3 x ^{5} y ^{2} z - 8 x ^{2} + 5 z ^{2} )}{- x ^{3} y ^{4} z ^{2}}

Cancel the common factor:

x^{3}

= \frac{y ^{4} z ^{3} ( 3 x ^{5} y ^{2} z - 8 x ^{2} + 5 z ^{2} )}{- y ^{4} z ^{2}}

Cancel the common factor:

y^{4}

= \frac{z ^{3} ( 3 x ^{5} y ^{2} z - 8 x ^{2} + 5 z ^{2} )}{- z ^{2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

z^{3} = z^{2} z

= \frac{z ^{2} z ( 3 x ^{5} y ^{2} z - 8 x ^{2} + 5 z ^{2} )}{- z ^{2}}

Cancel the common factor:

z^{2}

= \frac{z ( 3 x ^{5} y ^{2} z - 8 x ^{2} + 5 z ^{2} )}{- 1}

Apply the fraction rule:

\frac{a}{- 1} = - a

= - z (3 x^{5} y^{2} z - 8 x^{2} + 5 z^{2})

- 3 x - 3

- 4 x - x

4 \cdot 3 \cdot 2

- 8 - 12

(a + h)^{2}

What is ((24x^8y^6z^4-64x^5y^4z^3+40x^3y^4z^5))/((-8x^3y^4z^2)) ?
The solution to ((24x^8y^6z^4-64x^5y^4z^3+40x^3y^4z^5))/((-8x^3y^4z^2)) is -z(3x^5y^2z-8x^2+5z^2)