What is expand (e^{3x}-1)*(4-x^2) ?

The solution to expand (e^{3x}-1)*(4-x^2) is 4e^{3x}-e^{3x}x^2-4+x^2

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expand (e^{3x}-1)*(4-x^2)

expand

(e^{3 x} - 1) \cdot (4 - x^{2})

4 e^{3 x} - e^{3 x} x^{2} - 4 + x^{2}

Solution steps

(e^{3 x} - 1) (4 - x^{2})

Apply FOIL method:

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

a = e^{3 x}, b = - 1, c = 4, d = - x^{2}

= e^{3 x} \cdot 4 + e^{3 x} (- x^{2}) + (- 1) \cdot 4 + (- 1) (- x^{2})

Apply minus-plus rules

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

= 4 e^{3 x} - e^{3 x} x^{2} - 1 \cdot 4 + 1 \cdot x^{2}

Simplify

4 e^{3 x} - e^{3 x} x^{2} - 1 \cdot 4 + 1 \cdot x^{2} : 4 e^{3 x} - e^{3 x} x^{2} - 4 + x^{2}

= 4 e^{3 x} - e^{3 x} x^{2} - 4 + x^{2}

\frac{( x ^{2} )}{( 6 + x ) ^{3}}

2 ((a + e) + (b + f))

\frac{( s - 1 ) ( s + 3 )}{s ( s + 4 ) ( s + 2 )}

\frac{d}{d x} ((x - 2) (x - 10)^{3}) + 11

y^{''} (x) + (1 + x) y

What is expand (e^{3x}-1)*(4-x^2) ?
The solution to expand (e^{3x}-1)*(4-x^2) is 4e^{3x}-e^{3x}x^2-4+x^2