What is expand (2x-1)sqrt(-x^2+x+2) ?

The solution to expand (2x-1)sqrt(-x^2+x+2) is 2xsqrt(-x^2+x+2)-sqrt(-x^2+x+2)

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expand (2x-1)sqrt(-x^2+x+2)

expand

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

2 x - x^{2} + x + 2 - - x^{2} + x + 2

Solution steps

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

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

Apply the distributive law:

a (b - c) = ab - a c

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

= - x^{2} + x + 2 \cdot 2 x - - x^{2} + x + 2 \cdot 1

Simplify

- x^{2} + x + 2 \cdot 2 x - - x^{2} + x + 2 \cdot 1 : 2 x - x^{2} + x + 2 - - x^{2} + x + 2

= 2 x - x^{2} + x + 2 - - x^{2} + x + 2

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

9 - x^{2} \cdot x^{2} - 4

\frac{5}{x} - \frac{3}{( x ^{2} + 2 x + 8 )}

(1 + sin (2 x))^{2}

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

What is expand (2x-1)sqrt(-x^2+x+2) ?
The solution to expand (2x-1)sqrt(-x^2+x+2) is 2xsqrt(-x^2+x+2)-sqrt(-x^2+x+2)