What is expand (y+b/a)*(e^{at}-b/a) ?

The solution to expand (y+b/a)*(e^{at}-b/a) is e^{at}y-(yb)/a+(e^{at}b)/a-(b^2)/(a^2)

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expand (y+b/a)*(e^{at}-b/a)

expand

(y + \frac{b}{a}) \cdot (e^{a t} - \frac{b}{a})

e^{a t} y - \frac{y b}{a} + \frac{e ^{a t} b}{a} - \frac{b ^{2}}{a ^{2}}

Solution steps

(y + \frac{b}{a}) (e^{a t} - \frac{b}{a})

Apply FOIL method:

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

a = y, b = \frac{b}{a}, c = e^{a t}, d = - \frac{b}{a}

= y e^{a t} + y (- \frac{b}{a}) + \frac{b}{a} e^{a t} + \frac{b}{a} (- \frac{b}{a})

Apply minus-plus rules

+ (- a) = - a

= e^{a t} y - y \frac{b}{a} + e^{a t} \frac{b}{a} - \frac{b}{a} \cdot \frac{b}{a}

Simplify

e^{a t} y - y \frac{b}{a} + e^{a t} \frac{b}{a} - \frac{b}{a} \cdot \frac{b}{a} : e^{a t} y - \frac{y b}{a} + \frac{e ^{a t} b}{a} - \frac{b ^{2}}{a ^{2}}

= e^{a t} y - \frac{y b}{a} + \frac{e ^{a t} b}{a} - \frac{b ^{2}}{a ^{2}}

g (\frac{m}{z} + \frac{n x}{l})

3 (x + \frac{1}{2})

2 (\frac{3 3}{2} + 3)

(3 x^{2} y^{4} + 2 x y) d x + (2 x^{3} y^{3} - x^{2}) d y

What is expand (y+b/a)*(e^{at}-b/a) ?
The solution to expand (y+b/a)*(e^{at}-b/a) is e^{at}y-(yb)/a+(e^{at}b)/a-(b^2)/(a^2)