Question 1 of 49beginner🧠 RememberShort Answer2 marks

Can you identify the terms, variables, and coefficients of this algebraic expression: 2x² + 5xy - 3y²?

Correct Answer

In an algebraic expression, the terms are the individual parts separated by addition or subtraction signs. The variables are the symbols (like x, y, l, w) used to represent unknown quantities, and the coefficients are the numerical factors multiplying the variables in each term.

For example, in the expression 2x² + 5xy - 3y², the terms are 2x², 5xy, and -3y². The variables are x and y, and the coefficients are 2, 5, and -3. Similarly, for the total cost expression 200l + 160w + 50lw, the terms are 200l, 160w, and 50lw. The variables are l and w, and the coefficients are 200, 160, and 50.

Exercise: Think and Reflect | Q: 1 | (Page 2)
For More Understanding

Explanation

The textbook defines an algebraic expression as a combination of numbers, variables, and operation symbols. It explicitly identifies the parts of the expression 2x² + 5xy - 3y², stating that 2x², 5xy, and -3y² are the terms, while 2, 5, and -3 are the coefficients. The variables are x and y. The same identification process applies to other expressions in the text, such as 200l + 160w + 50lw, where 200l, 160w, and 50lw are the terms; l and w are the variables; and 200, 160, and 50 are the coefficients.

Solution Steps

  1. Step 1: Define terms as the individual parts of an algebraic expression separated by '+' or '-' signs (e.g., 2x², 5xy, -3y²).

  2. Step 2: Define variables as the symbols representing unknown values (e.g., x, y, l, w).

  3. Step 3: Define coefficients as the numerical factors multiplying the variables in each term (e.g., 2, 5, -3, 200, 160, 50).

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