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Chapter 10: Algebraic Expressions

    Introduction

    How are Expressions Formed

    Terms of an Expression

    Factors of a term

    Coefficients

    Like and Unlike Terms

    Monomials, Binomials, Trinomials and Polynomials

    Finding the Value of an Expression

    Exercise 10.1

    Exercise 10.2

    What Have We Discussed ?

    Extra Curriculum Support

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Chapter 10: Algebraic Expressions > How are Expressions Formed

How are Expressions Formed

In algebra, our primary tools are variables and constants, which we combine in various ways to create algebraic –to be filled by the user expressions. Variables, represented by letters like x, y, a, b, etc., are in nature, meaning their values can vary.

In contrast, constants are values, such as 5, -3, 100, and so forth.

To craft algebraic expressions, we use operations like addition, subtraction , multiplication , and division.

For instance, consider the expression 5x + 7.

Here, we multiply the variable x by the constant and then add the constant .

Another example is 3a - 4b.

In this case, we multiply variable a by and variable b by , and then subtract the latter from the former.

These expressions demonstrate how we can blend constants and variables to represent various mathematical relationships.

Moreover, algebraic expressions can also be formed by combining variables with themselves or with other variables.

For example: x² - y² is an expression where each variable is squared

("Squared" in mathematics refers to the operation of multiplying a number or a variable by itself. The term "squared" comes from the geometric concept where a square's area is calculated) and then subtracted from each other.

Another example is 2xy:

where we multiply two different variables, x and y, together. These combinations offer more complexity and versatility in algebra, allowing us to model a wide range of mathematical scenarios.

(i)x2

Instruction

The expression x2 is obtained by multiplying the variable x by itself.
x × x =
Just as 4 × 4 is written as , we write x × x = . It is commonly read as x squared.
In the same manner, we can write: x × x × x =
Commonly x3 is read as ‘x cubed’. Later, you will realise that x3 may also be read as "x raised to the power 3".
x,x2,x3 ... are all algebraic expressions obtained from x.

(ii)2y2

The expression 2y2 is obtained from y
2y2 = × × (Enter integer value first)
Here by multiplying y with y we obtain y2 and then we multiply y2 by the constant .

(iii)3x2−5

In (3x2- 5) we first obtain x2, and multiply it by 3 to get 3x2.
From 3x2, we 5 to finally arrive at 3x2- 5.

Describe how the following expressions are obtained: 7xy + 5, x2y, 4x2 – 5x.

Instruction

(i)7xy + 5

7xy + 5, we first obtain .
it by 7 to get 7xy.
And 5 to 7xy to get the expression 7xy + 5.

(ii)x2y

x2y, we obtain x2
it by y to get x2y.

(iii)4x2 - 5x

4x2 - 5x, we first obtain x2
it by 4 to get 4x2.
And obtain second term by x by constant 5.
From 4x2, we 5x to finally arrive at 4x2 - 5x.