What is expand (-1+3(dy)/(dx))(x-3) ?

The solution to expand (-1+3(dy)/(dx))(x-3) is -x+3+3x(dy)/(dx)-9(dy)/(dx)

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expand (-1+3(dy)/(dx))(x-3)

expand

(- 1 + 3 \frac{d y}{d x}) (x - 3)

- x + 3 + 3 x \frac{d y}{d x} - 9 \frac{d y}{d x}

Solution steps

(- 1 + 3 \frac{d y}{d x}) (x - 3)

Apply FOIL method:

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

a = - 1, b = 3 \frac{d y}{d x}, c = x, d = - 3

= (- 1) x + (- 1) (- 3) + 3 \frac{d y}{d x} x + 3 \frac{d y}{d x} (- 3)

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= - 1 \cdot x + 1 \cdot 3 + 3 x \frac{d y}{d x} - 3 \cdot 3 \frac{d y}{d x}

Simplify

- 1 \cdot x + 1 \cdot 3 + 3 x \frac{d y}{d x} - 3 \cdot 3 \frac{d y}{d x} : - x + 3 + 3 x \frac{d y}{d x} - 9 \frac{d y}{d x}

= - x + 3 + 3 x \frac{d y}{d x} - 9 \frac{d y}{d x}

- ln (sin (x)) cos (x) + sin (x) (- x - cot (x))

- \frac{4 ( e ^{2 i t} - e ^{- 2 i t} )}{5}

\frac{1}{25} (- 5 e^{- 5 x} x - e^{- 5 x})

\frac{1}{( 2 x + 7 ) ^{6}}

l im x \Rightarrow 2 (x^{2} - 3 x + 1)

What is expand (-1+3(dy)/(dx))(x-3) ?
The solution to expand (-1+3(dy)/(dx))(x-3) is -x+3+3x(dy)/(dx)-9(dy)/(dx)