What is expand 2(2xy^2+x^22y(dy)/(dx)) ?

The solution to expand 2(2xy^2+x^22y(dy)/(dx)) is 4xy^2+4x^2y(dy)/(dx)

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expand 2(2xy^2+x^22y(dy)/(dx))

expand

2 (2 x y^{2} + x^{2} 2 y \frac{d y}{d x})

4 x y^{2} + 4 x^{2} y \frac{d y}{d x}

Solution steps

2 (2 x y^{2} + x^{2} \cdot 2 y \frac{d y}{d x})

= 2 (2 x y^{2} + 2 x^{2} y \frac{d y}{d x})

Apply the distributive law:

a (b + c) = ab + a c

a = 2, b = 2 x y^{2}, c = x^{2} \cdot 2 y \frac{d y}{d x}

= 2 \cdot 2 x y^{2} + 2 x^{2} \cdot 2 y \frac{d y}{d x}

= 2 \cdot 2 x y^{2} + 2 \cdot 2 x^{2} y \frac{d y}{d x}

Multiply the numbers:

2 \cdot 2 = 4

= 4 x y^{2} + 4 x^{2} y \frac{d y}{d x}

(a + b \cdot i)^{3}

(x - 1 - x^{2})^{2}

33 (539 - 4)

(y^{2} + \frac{1}{4 y ^{2}})^{2}

\frac{2}{9} (3 k - 1)

What is expand 2(2xy^2+x^22y(dy)/(dx)) ?
The solution to expand 2(2xy^2+x^22y(dy)/(dx)) is 4xy^2+4x^2y(dy)/(dx)