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Exercise 8.1 class 8 solution-Introduction
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Exercise 8.1 class 8 solution-what is algebric expression ?
An algebraic expression is a mathematical expression that consists of numbers, variables, and mathematical operations (like addition, subtraction, multiplication, and division). Algebraic expressions are used to represent relationships and perform calculations in algebra, a branch of mathematics that deals with symbols and the rules for manipulating them. Algebraic expressions do not contain equality signs (e.g., “=”); instead, they describe mathematical relationships or operations.
umbers: These are constants or numerical values, such as 5, -3.14, or 7. Numbers in an algebraic expression do not change and are often referred to as coefficients.
Variables: Variables are symbols that represent unknown or varying values. Common variables are denoted by letters like x, y, a, or b. Variables can take on different values, and the goal is often to find the values of these variables that satisfy certain conditions.
Mathematical Operations: Algebraic expressions can involve various mathematical operations, such as addition (+), subtraction (-), multiplication (*), division (/), exponentiation (^), and more. These operations are used to perform calculations on numbers and variables within the expression.
Here are some examples of algebraic expressions:
- 3x + 2: This expression involves a variable (x) and uses addition and multiplication operators.
- 4y – 7: This expression also involves a variable (y) and uses subtraction.
- (x + 2)(x – 3): This is an example of a more complex algebraic expression that includes variables and multiplication inside parentheses.
Exercise 8.1 class 8 solution-Terms factor and coefficient.
- In algebra, a term is a single mathematical expression or component within an algebraic expression.
- An algebraic term can be a constant, a variable, or the product of constants and variables. It may also include exponents or coefficients.
- For example, in the expression 3x^2y, there are two terms: “3x^2” and “y.” “3x^2” is a term containing the variable x raised to the power of 2, and “y” is another term.
- A factor is a number, variable, or algebraic expression that is multiplied with another number, variable, or expression to produce a product.
- In the context of factoring in algebra, factors are the parts of an expression that, when multiplied together, give the original expression.
- For example, in the expression 3x(x + 2), the factors are 3, x, and (x + 2). These factors can be multiplied to obtain the original expression.
- A coefficient is the numerical part of a term in an algebraic expression, usually placed in front of a variable. It represents the constant multiplier of the variable.
- Coefficients can be whole numbers, fractions, decimals, or even negative numbers.
- For example, in the expression 4x, the coefficient is 4, and in the expression -0.5y, the coefficient is -0.5.
Exercise 8.1 class 8 solution- Monomial,Binomials,Trinomial.
- A monomial is an algebraic expression consisting of a single term. This term can include numbers, variables, and exponents, all multiplied together.
- Examples of monomials:
- 5x (consisting of the number 5 and the variable x)
- -2y^2 (consisting of the number -2 and the variable y squared)
- A binomial is an algebraic expression that consists of exactly two terms separated by either addition or subtraction.
- Examples of binomials:
- 3x + 2y (consisting of the two terms 3x and 2y, connected by addition)
- 4a – 7b (consisting of the two terms 4a and 7b, connected by subtraction)
- A trinomial is an algebraic expression that consists of exactly three terms separated by either addition or subtraction.
- Examples of trinomials:
- x^2 + 2x – 1 (consisting of the three terms x^2, 2x, and -1, connected by addition and subtraction)
- 2m^3 – 5m^2 + 3m (consisting of the three terms 2m^3, -5m^2, and 3m, connected by addition and subtraction)
Example 8.1.1 Add the expression :7xy+5yz-3zx , 4xy+7zx and 3yz+4.
Example 8.1.2 Subtract 5a^2–3ab+4b-7 from 8a^2 -3b^2 -8ab+9a-7b
Example 8.1.3 Subtract x+3y-5z+7 from the sum of the expressions 2x -3y+4z-2 and -3x+8y+12z-4.
Exercise 8.1 class 8 solution- Definition of like terms and unlike terms
- Like terms are terms in an algebraic expression that have the same variable(s) raised to the same power(s).
- Like terms can be added or subtracted from each other because they represent quantities that can be combined.
- Examples of like terms:
- 2x and 3x (both have the variable x with an exponent of 1)
- 4y^2 and 7y^2 (both have the variable y with an exponent of 2)
- Unlike terms are terms in an algebraic expression that have different variables, different variable exponents, or both.
- Unlike terms cannot be directly added or subtracted from each other because they represent different quantities or measurements.
- Examples of unlike terms:
- 4x and 3y (different variables, x and y)
- 5a^2 and 2b^2 (different variables and different exponents, a^2 and b^2)
Exercise 8.1 class 8 solution- exercise preview
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Exercise 8.1 class 8 solution- solution pdf
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