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The distributive property is a foundational algebraic concept that helps simplify expressions, especially when dealing with multiplication over addition or subtraction. This property states that when a term is multiplied by a group of terms inside parentheses, the outer term can be distributed to each of the items within, individually. For example, if you have the expression \(a(b + c)\), the distributive property allows you to rewrite it as \(ab + ac\). In other words, you are distributing the multiplication of \(a\) over both \(b\) and \(c\).
In the provided exercise, we see \(-3s(s^2 - 5t)\). Applying the distributive property involves:

• Multiplying \(-3s\) by \(s^2\)
• Multiplying \(-3s\) by \(-5t\)

After applying the distributive property, you'll have two separate terms that can later be combined.

Algebraic expressions are mathematical phrases involving numbers, variables, and operation symbols. They form the backbone of algebra and require understanding of how to manipulate these combinations to solve equations or simplify expressions.When dealing with algebraic expressions, it's essential to recognize the different components:

• **Terms**: The individual parts of the expression separated by \(+\) or \(-\), like \(-3s^3\) or \(15st\).
• **Coefficients**: The numerical factor in a term, such as \(-3\) in \(-3s^3\).
• **Variables**: The symbols that represent numbers, like \(s\) and \(t\) in the given example.

Understanding how these components interact underpins much of algebraic manipulation.

In algebra, mathematical operations such as addition, subtraction, multiplication, and division occur between terms and entire expressions. Each operation has its rules and affects expressions differently, especially when variables and coefficients are involved.In the exercise at hand, multiplication is the key operation:

• **Multiplication of Variables**: When \(-3s\) is multiplied by \(s^2\), the exponents of \(s\) are added: \(-3s \times s^2 = -3s^{1+2} = -3s^3\).
• **Multiplication with Constants**: Multiplying \(-3s\) by \(-5t\) involves multiplying coefficients and then attaching the variables: \(-3 \times -5 = 15\), resulting in \(15st\).

After these multiplications, combing the results gives the simplified expression. This operation illustrates how varying mathematical rules apply in multiplying and simplifying expressions.