What is (16x^6y^5z-12x^4y^6z^2+6x^3y^9)/(-4x^2y) ?

The solution to (16x^6y^5z-12x^4y^6z^2+6x^3y^9)/(-4x^2y) is -(xy^4(8x^3z-6xyz^2+3y^4))/2

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simplify (16x^6y^5z-12x^4y^6z^2+6x^3y^9)/(-4x^2y)

simplify

\frac{16 x ^{6} y ^{5} z - 12 x ^{4} y ^{6} z ^{2} + 6 x ^{3} y ^{9}}{- 4 x ^{2} y}

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

Solution steps

\frac{16 x ^{6} y ^{5} z - 12 x ^{4} y ^{6} z ^{2} + 6 x ^{3} y ^{9}}{- 4 x ^{2} y}

Factor out common term

2 x^{3} y^{5} : 2 x^{3} y^{5} (8 x^{3} z - 6 x y z^{2} + 3 y^{4})

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

Factor the number:

4 = 2 \cdot 2

= \frac{2 x ^{3} y ^{5} ( 8 x ^{3} z - 6 x y z ^{2} + 3 y ^{4} )}{- 2 \cdot 2 x ^{2} y}

Cancel the common factor:

2

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

Apply exponent rule:

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

x^{3} = x^{2} x

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

Cancel the common factor:

x^{2}

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

Apply exponent rule:

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

y^{5} = y y^{4}

= \frac{x y y ^{4} ( 8 x ^{3} z - 6 x y z ^{2} + 3 y ^{4} )}{- 2 y}

Cancel the common factor:

y

= \frac{x y ^{4} ( 8 x ^{3} z - 6 x y z ^{2} + 3 y ^{4} )}{- 2}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{x y ^{4} ( 8 x ^{3} z - 6 x y z ^{2} + 3 y ^{4} )}{2}

4 x^{2} + 9 y^{2} - 12 x y

(x - 1) \cdot (x - 2)

\frac{72}{180}

- 5 (3 p + 3) + 9 (- 7 + p)

3 lo g_{10} (4)

What is (16x^6y^5z-12x^4y^6z^2+6x^3y^9)/(-4x^2y) ?
The solution to (16x^6y^5z-12x^4y^6z^2+6x^3y^9)/(-4x^2y) is -(xy^4(8x^3z-6xyz^2+3y^4))/2