key term - Distributing

Definition

Distributing is the process of spreading or dividing something, such as a mathematical expression or equation, across multiple parts or terms. It is a fundamental skill in algebra that involves applying operations, like multiplication or division, to individual components within an expression to simplify or evaluate it.

5 Must Know Facts For Your Next Test

1. Distributing is often used when solving for a specific variable in a formula or equation, as it can help isolate the variable of interest.
2. The distributive property of multiplication states that $a(b + c) = ab + ac$, which is a key concept in distributing expressions.
3. Distributing can be used to expand expressions, such as $(x + y)^2 = x^2 + 2xy + y^2$, or to simplify expressions, such as $3(2x - 5) = 6x - 15$.
4. Proper distribution of variables and coefficients is essential for accurately solving equations and formulas for a specific variable.
5. Distributing can also be used to simplify complex fractions, such as $\frac{3x + 6}{2} = \frac{3x}{2} + \frac{6}{2}$.

Review Questions

• Explain how distributing can be used to solve a formula for a specific variable.
  • When solving a formula for a specific variable, distributing can be a useful technique to isolate that variable. By distributing the operations across the terms in the formula, you can rearrange the expression to get the variable of interest on one side of the equation. This allows you to solve for that variable and find its value in terms of the other variables and constants in the formula.
• Describe how the distributive property of multiplication relates to distributing expressions.
  • The distributive property of multiplication, which states that $a(b + c) = ab + ac$, is a fundamental concept in distributing expressions. This property allows you to distribute a coefficient or variable across the terms in an expression, making it easier to simplify or evaluate the expression. Understanding and applying the distributive property is crucial when distributing expressions, as it ensures that the resulting expression is equivalent to the original.
• Analyze how distributing can be used to expand or simplify complex algebraic expressions.
  • Distributing can be used both to expand and simplify algebraic expressions. When expanding an expression, such as $(x + y)^2$, distributing the exponent or multiplication across the terms can result in a more complex but equivalent expression, like $x^2 + 2xy + y^2$. Conversely, when simplifying an expression, distributing can help combine like terms and reduce the expression to a simpler form, as seen in the example $3(2x - 5) = 6x - 15$. Mastering the skill of distributing is essential for manipulating and working with a wide range of algebraic expressions.

Related terms

Factoring:

The process of breaking down an expression into a product of its factors, which can make it easier to simplify or evaluate.

Combining Like Terms:

The process of adding or subtracting terms in an expression that have the same variable or variables raised to the same power.

Simplifying Expressions: The process of reducing an algebraic expression to its simplest form by performing operations like distributing, factoring, and combining like terms.