What is factor 16x^5*y^2-8x^2*y-24x^4*y^2-40x^4*y^3 ?

The solution to factor 16x^5*y^2-8x^2*y-24x^4*y^2-40x^4*y^3 is 8x^2y(2x^3y-1-3x^2y-5x^2y^2)

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factor 16x^5y^2-8x^2y-24x^4y^2-40x^4y^3

factor

16 x^{5} \cdot y^{2} - 8 x^{2} \cdot y - 24 x^{4} \cdot y^{2} - 40 x^{4} \cdot y^{3}

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

Solution steps

16 x^{5} y^{2} - 8 x^{2} y - 24 x^{4} y^{2} - 40 x^{4} y^{3}

Apply exponent rule:

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

x^{5} y^{2} = x^{2} x^{3} yy, x^{4} y^{2} = x^{2} x^{2} yy, x^{4} y^{3} = x^{2} x^{2} y y^{2}

= 16 x^{2} x^{3} yy - 8 x^{2} y - 24 x^{2} x^{2} yy - 40 x^{2} x^{2} y y^{2}

Rewrite

- 40

5 \cdot 8

Rewrite

- 24

3 \cdot 8

= 2 \cdot 8 x^{2} x^{3} yy - 8 x^{2} y + 3 \cdot 8 x^{2} x^{2} yy + 5 \cdot 8 x^{2} x^{2} y y^{2}

Factor out common term

8 x^{2} y

= 8 x^{2} y (2 x^{3} y - 1 - 3 x^{2} y - 5 x^{2} y^{2})

- x^{2} + 5 x^{2} + 2 x - 24

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

25 x^{2} + 90 x y + 81 y^{2}

3 sin^{2} (a) - 6 - 3 cos^{2} (a)

x^{2} + 2 3 x + 3

What is factor 16x^5*y^2-8x^2*y-24x^4*y^2-40x^4*y^3 ?
The solution to factor 16x^5*y^2-8x^2*y-24x^4*y^2-40x^4*y^3 is 8x^2y(2x^3y-1-3x^2y-5x^2y^2)