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Popular >

simplify e^2(e-1)^2

Solution

simplify

e^{2} (e - 1)^{2}

Solution

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

+1

Decimal Notation

21.81613 \dots

Solution steps

e^{2} (e - 1)^{2}

Apply exponent rule:

a^{m} b^{m} = (ab)^{m}

e^{2} (e - 1)^{2} = (e (e - 1))^{2}

= (e (e - 1))^{2}

e (e - 1) = e^{2} - e

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

Apply Perfect Square Formula:

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

a = e^{2}, b = e

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

Simplify

(e^{2})^{2} - 2 e^{2} e + e^{2} : e^{4} - 2 e^{3} + e^{2}

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

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Frequently Asked Questions (FAQ)

What is e^2(e-1)^2 ?
The solution to e^2(e-1)^2 is e^4-2e^3+e^2