What is expand (4-x)^{1/2}(1+2x)^2 ?

The solution to expand (4-x)^{1/2}(1+2x)^2 is (4-x)^{1/2}+(4-x)^{1/2}*4x+(4-x)^{1/2}*4x^2

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expand (4-x)^{1/2}(1+2x)^2

expand

(4 - x)^{\frac{1}{2}} (1 + 2 x)^{2}

(4 - x)^{\frac{1}{2}} + (4 - x)^{\frac{1}{2}} \cdot 4 x + (4 - x)^{\frac{1}{2}} \cdot 4 x^{2}

Solution steps

(4 - x)^{\frac{1}{2}} (1 + 2 x)^{2}

Expand

(1 + 2 x)^{2} : 1 + 4 x + 4 x^{2}

= (4 - x)^{\frac{1}{2}} (1 + 4 x + 4 x^{2})

Apply the distributive law:

m (a + b + c) = ma + mb + m c

(4 - x)^{\frac{1}{2}} (1 + 4 x + 4 x^{2}) = (4 - x)^{\frac{1}{2}} \cdot 1 + (4 - x)^{\frac{1}{2}} \cdot 4 x + (4 - x)^{\frac{1}{2}} \cdot 4 x^{2}

= (4 - x)^{\frac{1}{2}} \cdot 1 + (4 - x)^{\frac{1}{2}} \cdot 4 x + (4 - x)^{\frac{1}{2}} \cdot 4 x^{2}

Apply rule:

a \cdot 1 = a

(4 - x)^{\frac{1}{2}} \cdot 1 = (4 - x)^{\frac{1}{2}}

= (4 - x)^{\frac{1}{2}} + (4 - x)^{\frac{1}{2}} \cdot 4 x + (4 - x)^{\frac{1}{2}} \cdot 4 x^{2}

(y^{\frac{7}{4}} - 1)^{4}

i (x + y i)^{4}

sin (2 t) \cdot x (t - π)

\frac{cos ^{2} ( x )}{( sin ( x ) + 1 ) ^{2}}

(1 - x^{\frac{2}{3}})^{3}

What is expand (4-x)^{1/2}(1+2x)^2 ?
The solution to expand (4-x)^{1/2}(1+2x)^2 is (4-x)^{1/2}+(4-x)^{1/2}*4x+(4-x)^{1/2}*4x^2