Question

Give me clear definition and examples of the following things in Algebra.

1. Constant
2. Variable
3. Algebraic expression
4. Term
5. A term of an expression
6. Monomial
7. Binomial
8. Trinomial
9. Polynomial
10. Factor
11. Coefficient
12. Numerical coefficient
13. Literal coefficient
14. Like term
15. Unlike term

Answer 1

I) CONSTANT : A symbol having a fixed numerical value is called constant . II) VARIABLE: a symbol which takes on various numberical value is known as variable.

CONSIDER THE FOLLOWING EXAMPLES :
The diameter d of a circle of radius r is given by the formula d= 2r.
Here, 2is a fixed number and, therefore, a constant, whereas the literal number d and r depend upon the size of the circle and, therefore, they may take on various values. so, d and r are variables.

III) ALGEBRAIC EXPRESSION : A combination of constant and variable connected by any one or more of the symbols is called algebraic expression.
Term : examples 3x + 5y- 2xyz are three terms.

IV) MONOMIAL: an expression contain only one term is known as a monomial.
Thus, 3x ,5xy ² ,2abc, -8, etc., are all monomial.
V) BINOMIAL :An expression containing two terms is called binomial.
Thus, 6-y, 2x+3y, x²- 5xy²z are all binomials.

VI) TRINOMIAL: a expression containing three terms is called trinomal.
Thus, 2+x-y, a+b+c, x³ -y³ +z³ are all trinomal.

VII) POLYNOMIAL : a expression containing two or more terms is called a polynomial.

VIII) FACTORS: when two or more numbers and literal are multuplied then each one of them is called a factor of its product.

IX) COEFFICIENT : In a product of numbers and literals, any of the factor is called coefficient of the products of other factors.

X) LIKE TERMS : a terms having the same literal factors are called like terms.
XI) UNLIKE TERMS : The terms not having same literal factors are called unlike terms.

EXAMPLE : In the expression 6x²y +5xy² -8xy -7yx² we have 6x²y and -7yx² as like terms, whereas 5xy² and -8xy are unlike terms.

Answer 2

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1. its value can't be changed
2. its value is unknown and can change
3. it is an expression with some variables in it
4. the different groups of numbers
5. its the same as term
6. an expression with only one term.eg-2
7. it has 2 terms
8. it has three terms
9. it has more than 3 terms
10. it is a number which exactly divides a number
11. it is the constant that accompanies a coefficient
12. it is a coefficient that is a number
13. it is literally a coefficient
14. similar terms
15. dissimilar terms

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