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Arithmetic Expressions - Simple Expressions

Grade 7CBSE

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

🔑Concepts

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An algebraic expression is formed from variables (like x,y,l,mx, y, l, m) and constants (like 3,4,−103, 4, -10) using arithmetic operations such as addition, subtraction, multiplication, and division.

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Expressions are made up of 'Terms'. For example, in the expression 4x2−3xy4x^2 - 3xy, the terms are 4x24x^2 and −3xy-3xy.

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A 'Factor' is what a term is broken down into. In the term 5xy5xy, the factors are 5,x,5, x, and yy.

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The numerical factor of a term is called its 'Numerical Coefficient' or simply 'Coefficient'. In the term −7xy-7xy, the coefficient is −7-7.

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Terms which have the same algebraic factors are called 'Like Terms'. For example, 2xy2xy and −5xy-5xy are like terms. Terms with different algebraic factors are 'Unlike Terms', such as 2x2x and 2y2y.

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Expressions are classified by the number of terms: 'Monomial' (one term), 'Binomial' (two terms), 'Trinomial' (three terms), and 'Polynomial' (one or more terms).

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To add or subtract algebraic expressions, we combine 'Like Terms' and keep 'Unlike Terms' as they are.

📐Formulae

General Linear Expression: ax+b\text{General Linear Expression: } ax + b

Addition of Like Terms: mx+nx=(m+n)x\text{Addition of Like Terms: } mx + nx = (m + n)x

Subtraction of Like Terms: mx−nx=(m−n)x\text{Subtraction of Like Terms: } mx - nx = (m - n)x

Value of expression at x=a:f(a)\text{Value of expression at } x=a: f(a)

💡Examples

Problem 1:

Identify the terms and their coefficients in the expression 5−3t25 - 3t^2.

Solution:

The terms are 55 and −3t2-3t^2. The coefficient of the term −3t2-3t^2 is −3-3. The term 55 is a constant.

Explanation:

Terms are separated by plus or minus signs. The numerical part multiplying the variable is the coefficient.

Problem 2:

Add the expressions: 7x2−4x+57x^2 - 4x + 5 and 9x−109x - 10.

Solution:

(7x2−4x+5)+(9x−10)=7x2+(−4x+9x)+(5−10)=7x2+5x−5(7x^2 - 4x + 5) + (9x - 10) = 7x^2 + (-4x + 9x) + (5 - 10) = 7x^2 + 5x - 5

Explanation:

We group the like terms together: x2x^2 terms, xx terms, and constant terms, then perform the arithmetic.

Problem 3:

Subtract 24ab−10b−18a24ab - 10b - 18a from 30ab+12b+14a30ab + 12b + 14a using vertical column method.

Solution:

30ab+12b+14a−(24ab−10b−18a)6ab+22b+32a\begin{array}{r} 30ab + 12b + 14a \\ -(24ab - 10b - 18a) \\ \hline 6ab + 22b + 32a \end{array}

Explanation:

In subtraction, change the sign of every term in the expression being subtracted and then add the terms column-wise.

Problem 4:

Find the value of the expression n3+5n2+5n−2n^3 + 5n^2 + 5n - 2 when n=−2n = -2.

Solution:

Substitute n=−2n = -2: (−2)3+5(−2)2+5(−2)−2(-2)^3 + 5(-2)^2 + 5(-2) - 2 =−8+5(4)−10−2= -8 + 5(4) - 10 - 2 =−8+20−10−2=0= -8 + 20 - 10 - 2 = 0

Explanation:

Replace the variable nn with the given value −2-2 and follow the order of operations (BODMAS/PEMDAS).