What is expand (e^{5x}-1)(4-x^2) ?

The solution to expand (e^{5x}-1)(4-x^2) is 4e^{5x}-e^{5x}x^2-4+x^2

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expand (e^{5x}-1)(4-x^2)

expand

(e^{5 x} - 1) (4 - x^{2})

4 e^{5 x} - e^{5 x} x^{2} - 4 + x^{2}

Solution steps

(e^{5 x} - 1) (4 - x^{2})

Apply FOIL method:

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

a = e^{5 x}, b = - 1, c = 4, d = - x^{2}

= e^{5 x} \cdot 4 + e^{5 x} (- x^{2}) + (- 1) \cdot 4 + (- 1) (- x^{2})

Apply minus-plus rules

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

= 4 e^{5 x} - e^{5 x} x^{2} - 1 \cdot 4 + 1 \cdot x^{2}

Simplify

4 e^{5 x} - e^{5 x} x^{2} - 1 \cdot 4 + 1 \cdot x^{2} : 4 e^{5 x} - e^{5 x} x^{2} - 4 + x^{2}

= 4 e^{5 x} - e^{5 x} x^{2} - 4 + x^{2}

\frac{1}{2} (lo g_{6} (x) + lo g_{8} (y))

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

\frac{2 ( 7 - 4 )}{3}

(\frac{b}{a} (x - z) + y + c)^{3}

l {e^{4 t} (t - cos (t))}

What is expand (e^{5x}-1)(4-x^2) ?
The solution to expand (e^{5x}-1)(4-x^2) is 4e^{5x}-e^{5x}x^2-4+x^2