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

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

Apply rule:

a \cdot 1 = a

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

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

- 2 x (x^{2} y cos (x^{2} y) + sin (x^{2} y))

\frac{7 x ^{2} - 23 x + 26}{( x + 2 ) ( x - 3 ) ^{2}}

\frac{4 p q ^{4} ( 7 p + 1 )}{5 r}

cos (k x - wt) + cos ((k + d k) x - (w + d w) t)

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

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