What is expand (e^{4x}-1)(36-x^2) ?

The solution to expand (e^{4x}-1)(36-x^2) is 36e^{4x}-e^{4x}x^2-36+x^2

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expand (e^{4x}-1)(36-x^2)

expand

(e^{4 x} - 1) (36 - x^{2})

36 e^{4 x} - e^{4 x} x^{2} - 36 + x^{2}

Solution steps

(e^{4 x} - 1) (36 - x^{2})

Apply FOIL method:

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

a = e^{4 x}, b = - 1, c = 36, d = - x^{2}

= e^{4 x} \cdot 36 + e^{4 x} (- x^{2}) + (- 1) \cdot 36 + (- 1) (- x^{2})

Apply minus-plus rules

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

= 36 e^{4 x} - e^{4 x} x^{2} - 1 \cdot 36 + 1 \cdot x^{2}

Simplify

36 e^{4 x} - e^{4 x} x^{2} - 1 \cdot 36 + 1 \cdot x^{2} : 36 e^{4 x} - e^{4 x} x^{2} - 36 + x^{2}

= 36 e^{4 x} - e^{4 x} x^{2} - 36 + x^{2}

x^{4} x + 3

(4 + 3 i)^{4}

(1 + 5 sin (t)) (5 cos (t))

\frac{d}{d x} ((x - 2) (x - 7)^{3}) + 8

\frac{( x - 3 ) ( x ^{2} + 9 ) ^{3}}{( 2 x - 5 ) ^{2}}

What is expand (e^{4x}-1)(36-x^2) ?
The solution to expand (e^{4x}-1)(36-x^2) is 36e^{4x}-e^{4x}x^2-36+x^2