CBSE Class 7 Mathematics Algebraic Expressions Notes Set 01

Terms, Factors and Coefficients

An algebraic expression is a combination of numbers and letters (variables) joined by the signs +, -, × and ÷. Parts joined by + or - are called terms. In a term, each number or letter multiplied together is a factor.
The number multiplying the letters is the numerical coefficient (in -6yz it is -6). Any factor can be called the coefficient of the remaining factors, so in 5yz the coefficient of z is 5y. When no number is written, the coefficient is 1, and for -y it is -1.

Kinds of Expressions

An expression with one term is a monomial, with two terms a binomial, and with three terms a trinomial. Any expression made of one or more terms is a polynomial.
Like terms have exactly the same letters with the same powers (5x² and -6x²). Unlike terms have different letter parts (2x and 5y, or 6xy² and 8x²y). The constant term has no letter.

Adding and Subtracting Expressions

Add or subtract only like terms, by adding or subtracting their coefficients. Unlike terms stay as they are. Arrange the answer with the highest power first.
To subtract an expression, change the sign of every term in it and then add. Questions such as what must be added to A to get B are solved by finding B - A, and what must be subtracted from A to get B by finding A - B.

Brackets and Value of an Expression

When simplifying, remove brackets from the innermost outwards, in the order ( ), { }, [ ]. A bracket with a minus sign before it changes the sign of every term inside; a plus sign leaves the signs unchanged. Follow BODMAS for the order of operations.
To find the value of an expression, simplify it and then replace each letter by the given number. Remember that (-1)² = 1, whereas -1² means -(1²).

Worked Example

Simplify \( 2x-[3y-\{2x-(y-x)\}] \).
Innermost bracket: 2x - (y - x) = 3x - y. Next: 3y - (3x - y) = 4y - 3x. Finally: 2x - (4y - 3x) = 5x - 4y.