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

The solution to expand (e^{2x}-5x)^2 is e^{4x}-10e^{2x}x+25x^2

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

expand

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

e^{4 x} - 10 e^{2 x} x + 25 x^{2}

Solution steps

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

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = e^{2 x}, b = 5 x

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

Simplify

(e^{2 x})^{2} - 2 e^{2 x} \cdot 5 x + (5 x)^{2} : e^{4 x} - 10 e^{2 x} x + 25 x^{2}

= e^{4 x} - 10 e^{2 x} x + 25 x^{2}

What is expand (e^{2x}-5x)^2 ?
The solution to expand (e^{2x}-5x)^2 is e^{4x}-10e^{2x}x+25x^2