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Algebraic Expressions - Finding the Value of an Expression

Grade 7CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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An algebraic expression consists of variables (letters like x,y,zx, y, z) and constants (numbers like 5,−105, -10) connected by arithmetic operations. Visually, imagine an expression like 2x+52x + 5 as a balance scale where xx represents an unknown weight in a box.

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The process of finding the value involves 'Substitution', which means replacing the variable with a given number. Visually, this is like removing a label 'x' and putting a physical number into its spot inside a pair of brackets.

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Expressions are made of 'Terms' which are separated by plus or minus signs. For example, in 3x2−4y3x^2 - 4y, the terms are 3x23x^2 and −4y-4y. Visually, you can represent this as a tree diagram where the expression is the trunk, the terms are the branches, and the factors are the leaves.

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A 'Coefficient' is the numerical factor of a term. In the term −7xy-7xy, the coefficient is −7-7. It tells you how many times the variable part is being multiplied.

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When substituting negative values, it is crucial to use parentheses to avoid sign errors. For instance, if x=−2x = -2, then x2x^2 should be written and calculated as (−2)2=4(-2)^2 = 4, rather than −22=−4-2^2 = -4.

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The value of an expression changes depending on the value assigned to the variable. If you plot this on a graph, different values of xx (on the horizontal axis) lead to different values of the expression (on the vertical axis).

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To evaluate complex expressions, follow the BODMAS/PEMDAS order of operations: Brackets, Orders (Exponents), Division and Multiplication, then Addition and Subtraction. This ensures a single, correct numerical result.

📐Formulae

Value of ax+bax + b at x=nx = n is a(n)+ba(n) + b

Value of x2x^2 when x=ax = a is (a)×(a)=a2(a) \times (a) = a^2

Value of xyxy when x=a,y=bx = a, y = b is a×ba \times b

Distributive Property: a(b+c)=ab+aca(b + c) = ab + ac

Perimeter of a square with side ss: P=4sP = 4s

Area of a square with side ss: A=s2A = s^2

💡Examples

Problem 1:

Find the value of the expression 7n−47n - 4 for n=3n = 3.

Solution:

Step 1: Write the expression: 7n−47n - 4\Step 2: Substitute n=3n = 3 into the expression: 7(3)−47(3) - 4\Step 3: Multiply the terms: 21−421 - 4\Step 4: Subtract the numbers: 1717\Therefore, the value of the expression is 1717.

Explanation:

We replace the variable nn with the number 33, then follow the order of operations by multiplying before subtracting.

Problem 2:

Evaluate x2−2xy+y2x^2 - 2xy + y^2 when x=2x = 2 and y=−1y = -1.

Solution:

Step 1: Substitute x=2x = 2 and y=−1y = -1 into the expression: (2)2−2(2)(−1)+(−1)2(2)^2 - 2(2)(-1) + (-1)^2\Step 2: Calculate the square of xx: 22=42^2 = 4\Step 3: Calculate the middle term: −2×2×(−1)=+4-2 \times 2 \times (-1) = +4\Step 4: Calculate the square of yy: (−1)2=1(-1)^2 = 1\Step 5: Add the results: 4+4+1=94 + 4 + 1 = 9\The final value is 99.

Explanation:

This problem involves two variables and powers. Pay close attention to the negative sign of yy; when you square −1-1 or multiply by it, the signs change according to integer multiplication rules.