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Please help simplify this function, high school level, will give brainliest :)

Please Help Simplify This Function High School Level Will Give Brainliest class=

Sagot :

nuhulawal20

The simplified form of the expression (( (-2 + h)³ + 8 ) / h) is h² - 6h + 12

What is the simplified form of the given expression?

Given the expression in question;

( (-2 + h)³ + 8 ) / h

First, we simplify the numerator.

Lets rewrite 8 as 2³

(-2 + h)³ + 2³

Now, we can use the sum of cubes formula to factorize since both terms are perfect cubes.

a³ + b³ = ( a + b )( a² - ab + b² )

(-2 + h)³ + 2³ = ( -2 + h + 2 )( (-2 + h)² - (-2 + h)2 + 2² )

(-2 + h)³ + 2³ = h( (-2 + h)² + 4 - 2h + 4 )

(-2 + h)³ + 2³ = h( (-2 + h)²- 2h + 8 )

(-2 + h)³ + 2³ = h( (h² - 4h + 4 )- 2h + 8 )

(-2 + h)³ + 2³ = h( h² - 4h + 4 - 2h + 8 )

(-2 + h)³ + 2³ = h( h² - 6h + 12 )

Now bring back the denominator.

( h( h² - 6h + 12 ) ) / h

Cancel the common factors h

h² - 6h + 12

Therefore, the simplified form of the expression (( (-2 + h)³ + 8 ) / h) is h² - 6h + 12

Learn more about  sum of cubes formula here: https://brainly.com/question/10367382

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