What is (e^x-3e^x)*(e^x-3e^x) ?

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

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simplify (e^x-3e^x)*(e^x-3e^x)

simplify

(e^{x} - 3 e^{x}) \cdot (e^{x} - 3 e^{x})

4 e^{2 x}

Solution steps

(e^{x} - 3 e^{x}) (e^{x} - 3 e^{x})

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

(e^{x} - 3 e^{x}) (e^{x} - 3 e^{x}) = (e^{x} - 3 e^{x})^{1 + 1}

= (e^{x} - 3 e^{x})^{1 + 1}

Add the numbers:

1 + 1 = 2

= (e^{x} - 3 e^{x})^{2}

Add similar elements:

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

= (- 2 e^{x})^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- 2 e^{x})^{2} = (2 e^{x})^{2}

= (2 e^{x})^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= 2^{2} (e^{x})^{2}

(e^{x})^{2} : e^{x \cdot 2}

= 2^{2} e^{x \cdot 2}

2^{2} = 4

= 4 e^{2 x}

- 6 t^{2} x^{2}

3 e^{- 2 t} cos (5 t)

a^{2} \cdot (a + c)^{2}

2 (\frac{1}{2} x^{5} y^{2}) (2 x^{2} y^{5})

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