What is expand 4(3x^2-2xy-5y^2)^2 ?

The solution to expand 4(3x^2-2xy-5y^2)^2 is 36x^4-48x^3y-104x^2y^2+80xy^3+100y^4

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expand 4(3x^2-2xy-5y^2)^2

expand

4 (3 x^{2} - 2 x y - 5 y^{2})^{2}

36 x^{4} - 48 x^{3} y - 104 x^{2} y^{2} + 80 x y^{3} + 100 y^{4}

Solution steps

4 (3 x^{2} - 2 x y - 5 y^{2})^{2}

(3 x^{2} - 2 x y - 5 y^{2})^{2} = 9 x^{4} - 12 x^{3} y - 26 x^{2} y^{2} + 20 x y^{3} + 25 y^{4}

= 4 (9 x^{4} - 12 x^{3} y - 26 x^{2} y^{2} + 20 x y^{3} + 25 y^{4})

Distribute parentheses

= 4 \cdot 9 x^{4} + 4 (- 12 x^{3} y) + 4 (- 26 x^{2} y^{2}) + 4 \cdot 20 x y^{3} + 4 \cdot 25 y^{4}

Apply minus-plus rules

+ (- a) = - a

= 4 \cdot 9 x^{4} - 4 \cdot 12 x^{3} y - 4 \cdot 26 x^{2} y^{2} + 4 \cdot 20 x y^{3} + 4 \cdot 25 y^{4}

Simplify

4 \cdot 9 x^{4} - 4 \cdot 12 x^{3} y - 4 \cdot 26 x^{2} y^{2} + 4 \cdot 20 x y^{3} + 4 \cdot 25 y^{4} : 36 x^{4} - 48 x^{3} y - 104 x^{2} y^{2} + 80 x y^{3} + 100 y^{4}

= 36 x^{4} - 48 x^{3} y - 104 x^{2} y^{2} + 80 x y^{3} + 100 y^{4}

\frac{3}{2} sin (2 x) (3 cos (2 x) - 1)

\frac{d}{d x} ((x + 6) \cdot e^{3 x}) + 4

(y - \frac{7}{4})^{2}

(4 x^{2} + x) e^{2 x + 2}

What is expand 4(3x^2-2xy-5y^2)^2 ?
The solution to expand 4(3x^2-2xy-5y^2)^2 is 36x^4-48x^3y-104x^2y^2+80xy^3+100y^4