What is factor 10x^2*y^3-5x^2*y^2+15x^3*y^3 ?

The solution to factor 10x^2*y^3-5x^2*y^2+15x^3*y^3 is 5x^2y^2(2y-1+3xy)

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factor 10x^2y^3-5x^2y^2+15x^3*y^3

factor

10 x^{2} \cdot y^{3} - 5 x^{2} \cdot y^{2} + 15 x^{3} \cdot y^{3}

5 x^{2} y^{2} (2 y - 1 + 3 x y)

Solution steps

10 x^{2} y^{3} - 5 x^{2} y^{2} + 15 x^{3} y^{3}

Apply exponent rule:

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

x^{2} y^{3} = x^{2} y^{2} y, x^{3} y^{3} = x^{2} x y^{2} y

= 10 x^{2} y^{2} y - 5 x^{2} y^{2} + 15 x^{2} x y^{2} y

Rewrite

15

3 \cdot 5

Rewrite

10

2 \cdot 5

= 2 \cdot 5 x^{2} y^{2} y - 5 x^{2} y^{2} + 3 \cdot 5 x^{2} x y^{2} y

Factor out common term

5 x^{2} y^{2}

= 5 x^{2} y^{2} (2 y - 1 + 3 x y)

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

(c^{2} d^{3} y^{- 4})^{0} (2 c^{3} d^{- 2} y^{3})

(x^{2} x)^{2}

a^{8.3} + c^{10.6} + 4 \cdot 7

(\frac{( d \cdot y ^{- 3} )}{( d ^{5} \cdot y )})^{- 4}

What is factor 10x^2*y^3-5x^2*y^2+15x^3*y^3 ?
The solution to factor 10x^2*y^3-5x^2*y^2+15x^3*y^3 is 5x^2y^2(2y-1+3xy)