What is (I-ED)(I+(ED)/(I-DE)) ?

The solution to (I-ED)(I+(ED)/(I-DE)) is I^2-EDI+ED

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simplify (I-ED)(I+(ED)/(I-DE))

simplify

(I - E D) (I + \frac{E D}{I - D E})

I^{2} - E D I + E D

Solution steps

(I - E D) (I + \frac{E D}{I - D E})

Join

I + \frac{E D}{I - D E} : \frac{I ^{2} - E D I + E D}{I - D E}

= (I - E D) \frac{I ^{2} - E D I + E D}{I - D E}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( I - E D ) ( I ^{2} - E D I + E D )}{I - D E}

Apply the commutative law:

I - D E = I - E D

= \frac{( I - E D ) ( I ^{2} - E D I + E D )}{I - E D}

Cancel the common factor:

I - E D

= I^{2} - E D I + E D

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What is (I-ED)(I+(ED)/(I-DE)) ?
The solution to (I-ED)(I+(ED)/(I-DE)) is I^2-EDI+ED