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The distributive property is a fundamental concept in algebra. It involves multiplying a single term by each term inside a set of parentheses. Consider this part of our original exercise: 8(2k - 1). To apply the distributive property, multiply 8 by each term inside the parentheses: - Multiply 8 by 2k to get 16k - Multiply 8 by -1 to get -8 Thus, 8(2k - 1) becomes 16k - 8. The distributive property helps simplify expressions and is key in solving many algebraic problems. Always remember, when you see parentheses, think about distributing.

Combining like terms is another essential algebraic skill. This process involves adding or subtracting terms with the same variable or constants. From our exercise, after applying the distributive property, we had: 16k - 8 - 4k + 3. We combine the terms with the same variables: - Combine 16k and -4k: 16k - 4k = 12k - Combine -8 and +3: -8 + 3 = -5 Combining like terms simplifies the expression to: 12k - 5. By grouping and simplifying terms this way, complex expressions become much easier to handle and solve.

An algebraic expression consists of numbers, variables, and operators. In our original exercise, the expression was: 8(2k - 1) - (4k - 3). This is a combination of constants (numbers) and variables (letters representing numbers). The objective when simplifying algebraic expressions is to make them as simple as possible by removing parentheses and combining like terms. To do this: - First, use the distributive property - Second, distribute any negative signs or constants - Finally, combine like terms Understanding and simplifying algebraic expressions is fundamental to solving equations and higher-level math problems. Regular practice with these steps will strengthen your algebra skills.