What is factor 15x^2y^2-3x^3y+75x^4 ?

The solution to factor 15x^2y^2-3x^3y+75x^4 is 3x^2(5y^2-xy+25x^2)

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factor 15x^2y^2-3x^3y+75x^4

factor

15 x^{2} y^{2} - 3 x^{3} y + 75 x^{4}

3 x^{2} (5 y^{2} - x y + 25 x^{2})

Solution steps

15 x^{2} y^{2} - 3 x^{3} y + 75 x^{4}

Apply exponent rule:

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

x^{3} y = x^{2} x, x^{4} = x^{2} x^{2}

= 15 x^{2} y^{2} - 3 x^{2} x + 75 x^{2} x^{2}

Rewrite

75

25 \cdot 3

Rewrite

15

5 \cdot 3

= 5 \cdot 3 x^{2} y^{2} - 3 x^{2} x + 25 \cdot 3 x^{2} x^{2}

Factor out common term

3 x^{2}

= 3 x^{2} (5 y^{2} - x y + 25 x^{2})

\frac{9 !}{2 ! ( 9 - 2 ) !}

6 x y^{4} (x^{2} y^{3})

0 = \frac{5}{2} x - \frac{5}{2} x^{2}

\frac{12 3}{3}

10 0^{\frac{5}{2}}

What is factor 15x^2y^2-3x^3y+75x^4 ?
The solution to factor 15x^2y^2-3x^3y+75x^4 is 3x^2(5y^2-xy+25x^2)