NCERT Solutions for Class 8 Maths Chapter 8 Algebraic Expressions and Identities

NCERT Solutions for Class 8 Maths Chapter 8 Algebraic Expressions and Identities are study tools that explain math problems with letters and numbers. These solutions help you understand terms, factors, and coefficients easily. By using algebraic expressions and identities class 8 questions and answers, students can solve complex sums and learn how to use special math formulas correctly.

Learning Terms and Basic Concepts

Math is like a game where we use letters to stand for numbers. In this chapter, we look at how to build these expressions. You will find that every expression has parts called terms. These terms are made of factors. A number used with a letter is called a coefficient. We don't want to get confused between these simple words. When we look at algebraic expressions and identities class 8 questions and answers, we see that these basics come up every single time.

If you see a term like 5xy, it means 5 times x times y. Here, 5 is the numerical coefficient. The letters x and y are the variables. We use these variables because we don't know the exact number yet. It's like a placeholder for a secret number. When we combine these terms using plus or minus signs, we create an expression.

• Variables: These are letters like x, y, or z. They can change their value.

• Constants: These are fixed numbers like 5, 10, or -3. They never change.

• Terms: These are added together to make an expression. For example, in 4x + 5, the terms are 4x and 5.

• Factors: These are the pieces multiplied to make a term. In 3ab, the factors are 3, a, and b.

If you are looking for algebraic expressions and identities class 8 questions and answers, you should know how to name them. We group them by how many terms they have. This helps us keep our work organized and tidy.

We must remember that a polynomial can have many terms. It doesn't just mean "four or more." Even a single term is a type of polynomial. This is a common thing students forget. When you use the algebraic expressions and identities class 8 questions and answers, you will see many examples of these different types.

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Adding and Subtracting Math Expressions

Adding expressions is like sorting toys into boxes. You can only add "Like Terms" together. These are terms that have the exact same letters. You cannot add 5x to 3y because they are different. We use NCERT Solutions for Class 8 Maths Chapter 8  Algebraic Expressions and Identities to practice this.

• Step 1: Write the expressions in a row or one below the other.

• Step 2: Find the terms that look the same (Like Terms).

• Step 3: Add or subtract the numbers in front of the letters.

When you do subtraction, be very careful. You must change the signs of the terms you are taking away. This is a vital part of solving algebraic expressions and identities class 8 questions and answers. We don't want to make small mistakes with plus and minus signs. Always group the letters together first before doing the math.

Multiplying Monomials and Simple Polynomials

Multiplying is different from adding. You can multiply any terms, even if they aren't "Like Terms." When we multiply letters, we add their powers. This is clearly shown in algebraic expressions and identities class 8 NCERT solutions.

• Monomial by Monomial: Multiply the numbers first, then the letters. (2x) times (3y) gives 6xy.

• Monomial by Binomial: The single term outside the bracket must "visit" every term inside.

• Example: 3x(y + 2) = 3xy + 6x.

Using Special Math Identity Formulas

An identity is an equation that is true for any value you put into it. It is like a shortcut rule. Instead of multiplying long brackets, we use these rules. They are the most important part of NCERT Solutions for Class 8 Maths Chapter 8  Algebraic Expressions and Identities.

1. (a + b)² = a² + 2ab + b²

2. (a - b)² = a² - 2ab + b²

3. (a + b)(a - b) = a² - b²

4. (x + a)(x + b) = x² + (a + b)x + ab

These formulas help us solve squares of numbers quickly. For example, to find 103 squared, we write it as (100 + 3)². Then we use the first rule. This trick is great for exams. It saves a lot of time and effort. We don't need to do long multiplication on paper.

Solving Class 8 Practical Problems

Now we apply what we learned. Most questions ask you to simplify or find the value of an expression. You might get a question where x = 2 and you have to find the answer. This is why algebraic expressions and identities class 8 questions and answers are so helpful for practice.

• Area of a Rectangle: Length times Breadth. If length is 5x and breadth is 3y, area is 15xy.

• Volume of a Box: Length times Breadth times Height.

• Simplifying: Combine all like terms and use identities to make the expression smaller.

Using algebraic expressions and identities class 8 NCERT solutions helps you see the steps. Don't skip steps while writing. Each line should show a clear change. This helps teachers understand your work. It also helps you find mistakes if your final answer is wrong.

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