91Ó°ÊÓ

Algebraic expressions are like sentences in mathematics. They combine numbers, variables, and operations without giving a specific outcome, until they are calculated or simplified further. In the expression given in the exercise, the algebraic expression is \(2x(a-x)\).

Here, we have terms involving variables and numbers:

• \(2x\) is a term that multiplies the variable \(x\) by 2.
• The part inside the parentheses, \((a-x)\), is another algebraic expression itself.

Understanding these expressions involves recognizing how to manipulate them using mathematical operations like addition, subtraction, multiplication, or division. This is essential when you are aiming to simplify or solve them. Algebraic expressions are foundational for progressing into solving equations and understanding more advanced mathematical topics. They help formulate problems and allow problem-solving in a structured manner.

Simplifying expressions means making them easier to work with or understand. It involves reducing them to their simplest form without changing their value. In the exercise, the use of the distributive property is a key tool for simplification.

Let's break it down:

• The expression \(2x(a-x)\) initially looks complicated with the parentheses and variables combined.
• By applying the distributive property, \(2x(a-x)\) simplifies to \(2ax - 2x^2\).

Now, the expression is easy to understand and use in further calculations or problem-solving. Simplifying helps in recognizing like terms and combining them, which leads to clearer and more concise expressions. It allows you to see patterns and make computations more manageable.

Mathematical operations—such as addition, subtraction, multiplication, and division—are the building blocks of any mathematical expression. They tell you how to manipulate numbers and variables within an expression. In the exercise, the main operation used is multiplication, facilitated by the distributive property.

To apply the distributive property to the expression \(2x(a-x)\):

• First, multiply \(2x\) by each term inside the parentheses.
  • \(2x * a\) results in \(2ax\).
  • \(2x * (-x)\) results in \(-2x^2\).

Understanding these operations allows you to break down complex expressions step-by-step. It involves performing operations in a specific order, which is guided by rules like BODMAS/BIDMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction). This logical approach makes math consistent and predictable in solving complex problems.