Algebraic Expressions: CBSE Class 7 Maths

What Are Algebraic Expressions?

An algebraic expression is a combination of constants, variables, and the four fundamental mathematical operations. Let's break this down. A variable is a letter (like x, y, a, b) that represents an unknown number. A constant is a number with a fixed value (like 5, -10, or 2/3). When we combine them, we get an expression.

Consider the expression 4x + 7.

• This expression is made of two terms: 4x and 7.
• Terms are the parts of an expression that are added or subtracted.
• In the term 4x, the number 4 is called the coefficient. It's the number multiplied by the variable.
• The letter x is the variable.
• The term 7 is a constant term because it has a fixed value and no variable attached to it.

Expressions don't have an equal sign (=). They are like mathematical phrases, not complete sentences. For example, 5y - 3z is an expression with two terms, 5y and -3z. The coefficient of y is 5, and the coefficient of z is -3.

Key Vocabulary in Algebra

Variable

A symbol (usually a letter like x, y, or t) that can represent different numerical values. Its value is not fixed.

Constant

A value that does not change. It is a fixed number, like 5, -9, or 2/3.

Term

A single number, a single variable, or numbers and variables multiplied together. Terms are separated by + or - signs. In 3x + 2y - 5, the terms are 3x, 2y, and -5.

Coefficient

The numerical factor in a term. In the term 7y, the coefficient is 7. In the term -z, the coefficient is -1.

Like Terms

Terms that have the same algebraic factors (the same variables raised to the same powers). For example, 2xy and -5xy are like terms.

Unlike Terms

Terms that have different algebraic factors. For example, 3x², 4y, and 5xy are all unlike terms.

How to Add and Subtract Algebraic Expressions

1. Step 1: Identify and Group Like Terms — First, look at the expressions you need to add or subtract. Scan through all the terms and place the ones with the same variable parts next to each other. For example, to add (3x + 2y + 5) and (4x - y), you would group them as (3x + 4x) + (2y - y) + 5.
2. Step 2: Combine Coefficients of Like Terms — For each group of like terms, add or subtract their numerical coefficients. The variable part stays exactly the same. In our example, for the 'x' terms, you calculate 3 + 4 = 7. For the 'y' terms, you calculate 2 - 1 = 1. The constant term 5 has no like term to combine with.
3. Step 3: Write the Final Simplified Expression — Write down the new terms to form the final expression. From our example, we get 7x + 1y + 5, which is written as 7x + y + 5. Remember, you cannot combine unlike terms like 7x, y, and 5 any further.
4. Special Tip for Subtraction — When you subtract an entire expression, you must change the sign of EVERY term in the expression being subtracted. For example, (5a + 3b) - (2a - b) becomes 5a + 3b - 2a + b. After this, you can follow the steps above to combine the like terms.

Common Mistakes to Avoid

• Combining Unlike Terms: A very common mistake! You can add 3x + 2x to get 5x, but you CANNOT add 3x + 2y. They are different kinds of items, like adding 3 apples and 2 oranges.
• Forgetting the Sign: The sign (+ or -) in front of a term is part of it. In the expression 2x - 5y, the second term is -5y, not 5y. Always carry the sign with the term.
• Errors in Subtraction: When subtracting an expression like (4a + 5) - (2a - 3), many students forget to distribute the minus sign to all terms inside the second bracket. It should become 4a + 5 - 2a + 3, not 4a + 5 - 2a - 3.
• Confusing x and x²: Remember that x and x² are unlike terms because their powers are different. They cannot be added or subtracted together.

Practice Questions with Solutions

• Q: Identify the terms and their coefficients for the expression: 5xyz² - 3zy. A: Step 1: Identify the terms. Terms are separated by + or - signs. So, the terms are 5xyz² and -3zy. Step 2: Find the coefficient for each term. The coefficient is the numerical part. For the term 5xyz², the coefficient is 5. For the term -3zy, the coefficient is -3. Final answer: The terms are 5xyz² and -3zy. Their respective coefficients are 5 and -3.
• Q: Add the expressions: 7x + 5y - 3z and 2y + z - 4x. A: Step 1: Write the expressions together and group like terms by arranging them. We can write this as (7x - 4x) + (5y + 2y) + (-3z + z). Step 2: Combine the coefficients of the like terms. For x: 7 - 4 = 3. For y: 5 + 2 = 7. For z: -3 + 1 = -2. Step 3: Write the new terms together to form the final expression. Final answer: The sum is 3x + 7y - 2z.
• Q: Subtract (4a - 7ab + 3b + 12) from (12a - 9ab + 5b - 3). A: Step 1: Write the subtraction problem. The word 'from' means the second expression comes first: (12a - 9ab + 5b - 3) - (4a - 7ab + 3b + 12). Step 2: Distribute the negative sign to every term in the second bracket. This changes the sign of each of those terms: 12a - 9ab + 5b - 3 - 4a + 7ab - 3b - 12. Step 3: Group the like terms: (12a - 4a) + (-9ab + 7ab) + (5b - 3b) + (-3 - 12). Step 4: Combine the like terms by adding/subtracting their coefficients: 8a - 2ab + 2b - 15. Final answer: 8a - 2ab + 2b - 15.
• Q: Find the value of the expression 3x² - 2x - 7 when x = -2. A: Step 1: Substitute the value of x into the expression. Replace every x with (-2), using brackets to be safe: 3(-2)² - 2(-2) - 7. Step 2: Calculate the exponent first (BODMAS rule). (-2)² = (-2) × (-2) = 4. The expression becomes 3(4) - 2(-2) - 7. Step 3: Perform the multiplications. 3(4) = 12 and -2(-2) = +4. The expression is now 12 + 4 - 7. Step 4: Perform addition and subtraction from left to right. 12 + 4 = 16. Then 16 - 7 = 9. Final answer: The value of the expression is 9.

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