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The distributive property is a fundamental concept in algebra that allows us to multiply a single term by terms inside a parenthesis. When you see an expression like a(b + c), the distributive property lets you expand it by multiplying 'a' with both 'b' and 'c'.

• This property can be expressed as: \( a(b + c) = ab + ac \).
• It helps us break down more complex expressions into simpler parts.

For instance, in the expression \(-3(5 - 2x)\), we distribute \(-3\) across both \(5\) and \(-2x\). The calculations are \(-3 \times 5 = -15\) and \(-3 \times (-2x) = 6x\).This simplifies the expression to \(-15 + 6x\).Utilizing the distributive property is essential to simplify expressions, especially when dealing with polynomials or more complex algebraic expressions. It makes solving and simplifying equations easier and more manageable.

Combining like terms is all about simplifying expressions by adding or subtracting terms that have the same variables raised to the same power.

• "Like terms" are terms that have identical variable parts. For example, \(3x\) and \(5x\) are like terms.
• Constant terms, such as numbers without attached variables, can also be combined with one another.

In the expression \(-2x - 15 + 6x\), focus on the terms with \('x'\). Here, \(-2x\) and \(6x\) are like terms.Adding them, we get \(4x\).Once combined, the expression simplifies to \(4x - 15\).Combining like terms not only makes expressions simpler but also easier to work with when solving equations or further simplifying expressions.

Expressions in algebra are combinations of numbers, variables, and mathematical operations. They are the building blocks of algebraic equations and inequalities.

• An expression might include terms like \(2x\), constants like 3, and operations such as addition or subtraction.
• Expressions can be manipulated using various algebraic properties, such as the distributive property or combining like terms.

When working with expressions, it's important to familiarize yourself with these components. Simplifying an expression often involves transforming it into an easier form by using properties and operations appropriately. For instance, by applying the distributive property and combining like terms, the expression \(-2x - 3(5 - 2x)\) is simplified to \(4x - 15\).Understanding expressions and how to simplify them is crucial for solving algebraic equations and for progressing in mathematics.