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Expanding and Simplifying the Expression: (1/2x-3)(x+4/3)
This article explores the process of expanding and simplifying the given expression: (1/2x-3)(x+4/3).
Expanding the Expression
To expand the expression, we will use the FOIL method:
First: Multiply the first terms of each binomial: (1/2x) * x = 1/2x² Outer: Multiply the outer terms of the binomials: (1/2x) * (4/3) = 2/3x Inner: Multiply the inner terms of the binomials: (-3) * x = -3x Last: Multiply the last terms of each binomial: (-3) * (4/3) = -4
Therefore, the expanded expression becomes: (1/2x² + 2/3x - 3x - 4)
Simplifying the Expression
To simplify the expression, combine like terms:
1/2x² + (2/3x - 3x) - 4
Simplify the coefficients of the x terms:
1/2x² - 7/3x - 4
Final Result
The simplified expression is: 1/2x² - 7/3x - 4
This is the expanded and simplified form of the original expression.