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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