What is expand (3x+pi/3)*((3pi)/4-2x) ?

The solution to expand (3x+pi/3)*((3pi)/4-2x) is -6x^2+(19pix}{12}+\frac{pi^2)/4

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expand (3x+pi/3)*((3pi)/4-2x)

expand

(3 x + \frac{π}{3}) \cdot (\frac{3 π}{4} - 2 x)

- 6 x^{2} + \frac{19 π x}{12} + \frac{π ^{2}}{4}

Solution steps

(3 x + \frac{π}{3}) (\frac{3 π}{4} - 2 x)

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = 3 x, b = \frac{π}{3}, c = \frac{3 π}{4}, d = - 2 x

= 3 x \frac{3 π}{4} + 3 x (- 2 x) + \frac{π}{3} \cdot \frac{3 π}{4} + \frac{π}{3} (- 2 x)

Apply minus-plus rules

+ (- a) = - a

= 3 \cdot \frac{3 π}{4} x - 3 \cdot 2 xx + \frac{π}{3} \cdot \frac{3 π}{4} - 2 \cdot \frac{π}{3} x

Simplify

3 \cdot \frac{3 π}{4} x - 3 \cdot 2 xx + \frac{π}{3} \cdot \frac{3 π}{4} - 2 \cdot \frac{π}{3} x : - 6 x^{2} + \frac{19 π x}{12} + \frac{π ^{2}}{4}

= - 6 x^{2} + \frac{19 π x}{12} + \frac{π ^{2}}{4}

e^{x^{3}} (3 x^{2} y - x^{2}) d x + e^{x^{3}} d y

\frac{2 ( x + 11 )}{( x - 5 ) ( x + 3 )}

(x + y) l e f t (x - y)

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

(3 x^{2} - \frac{1}{x ^{3}})^{10}

What is expand (3x+pi/3)*((3pi)/4-2x) ?
The solution to expand (3x+pi/3)*((3pi)/4-2x) is -6x^2+(19pix}{12}+\frac{pi^2)/4