Page 107 - Start Up Mathematics_7

Brainstorming

Match the following:
5
5
(a) A polynomial of degree 5 (i) 2a + 3b + 4
5
5
(b) An algebraic expression consisting of (ii) 3a + 7bc – a
unlike terms of the same degree
5
5
(c) The perimeter of a triangle with sides (iii) 2a + 3b + 6
5
5
5
a + 1, 3 + 2b and a + b 5
4
5
5
5
5
5
(d) The sum of a + b + 3 and a + 2b + 2 (iv) a + 3a + 2a 2
3 2
3 2
3 2
(e) A binomial (v) a b + b c + c a
5
5
5
5
(f) In a class having (2a + 3b + 36) students, 30 are (vi) 2a + 3b + 5
girls. The expression denoting number of boys is
At a Glance
1. Letters of alphabet like x, y, l, m, ... representing numbers are called literals. Since the letters
stand for unknown numbers which can take different values, hence literals are variables.
2. A number having fixed numerical value is called a constant.
3. A combination of literals (variables) and constants connected by signs of fundamental operations
(+, –, ×, ÷) are called algebraic expressions.
4. An algebraic expression is made up of terms connected by + or – signs.
5. A term is a product of factors.
6. In an algebraic expression, the coefficient is either a numerical factor or an algebraic factor
or product of both.
7. The terms having exactly the same variable or algebraic factors (i.e., literals) are called like
terms. The terms not having the same variable factors are called unlike terms.

8. An algebraic expression in which none of the terms have negative or fractional exponent for
any variable is called a polynomial. In a polynomial power of x is a non-negative integer.
9. A polynomial having one, two and three terms is called monomial, binomial and trinomial
respectively.
10. The highest power in all the terms of an algebraic expression is called the degree of the
polynomial.
11. To add algebraic expressions, we regroup the like terms in one bracket and sum them up
in order to get another like term with coefficient equal to the sum of the coefficients of like
terms. The unlike terms are not added to each other to get a new term but they are joined
with + signs in between.
12. To subtract an algebraic expression from another, we add the additive inverse of the
expression to be subtracted, i.e., we change the signs of all the terms of the expression to be
subtracted and add them to the other algebraic expression.
13. The value of an expression depends on the value of the variables involved in it.

14. Algebraic expressions come very handy in writing rules and formulas.

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