Algebraic Expressions and Identities - Exercise 6.1 | Mathematics (Maths) Class 8 PDF Download

 Page 1


Q u e s t i o n : 1
Identify the terms, their coefficients for each of the following expressions:
i 7x
2
yz - 5xy
ii x
2
 + x + 1
iii 3x
2
y
2
 - 5x
2
y
2
z
2
 + z
2
iv 9 - ab + bc - ca
v 
a
2
+
b
2
-ab
vi 0.2x - 0.3xy + 0.5y
S o l u t i o n :
D e f i n i t i o n s :
A t e r m in an algebraic expression can be a constant, a variable or a product of constants and variables separated by the signs of addition + or subtraction (-) . Examples: 27, x, xyz, 
1
2
x
2
yz etc.
The number factor of the term is called its c o e f f i c i e n t.
i The expression 7x
2
yz -5xy consists of two terms, i.e.,  7x
2
yz and -5xy.
The coefficient of 7x
2
yz is 7 and the coefficient of -5xy is -5.
ii The expression x
2
+x +1 consists of three terms , i.e., ? x
2
, x and 1.
The coefficient of each term is 1.
iii The expression 3x
2
y
2
-5x
2
y
2
z
2
+z
2
 consists of three terms , i.e., ? 3x
2
y
2
, -5x
2
y
2
z
2
 and  z
2
. The coefficient of 3x
2
y
2
 is 3. The coefficient of -5x
2
y
2
z
2
 is -5 and the coefficient of z
2
 is 1.
iv The expression 9 -ab +bc -ca consists of four terms — 9, -ab, bc and -ca. The coefficient of the term 9 is 9. The coefficient of -ab is -1. The coefficient of bc is 1, and the coefficient of 
-ca is -1.
v The expression 
a
2
+
b
2
-ab consists of three terms , i.e., ? 
a
2
, 
b
2
 and -ab. The coefficient of 
a
2
 is 
1
2
. The coefficient of 
b
2
 is 
1
2
, and the coefficient of -ab is -1.
vi The expression 0. 2x -0. 3xy +0. 5y consists of three terms , i.e., ? 0. 2x, -0. 3xy and 0. 5y. The coefficient of 0. 2x is 0. 2. The coefficient of -0. 3xy is -0. 3, and the coefficient of 0. 5y is 
0. 5.
Q u e s t i o n : 2
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category?
i x + y
ii 1000
iii x + x
2
 + x
3
 + 4y
4
iv 7 + a + 5b
v 2b - 3b
2
vi 2y - 3y
2
 + 4y
3
vii 5x - 4y + 3x
viii 4a - 15a
2
ix xy + yz + zt + tx
x pqr
xi p
2
q + pq
2
xii 2p + 2q
S o l u t i o n :
Definitions:
A polynomial is m o n o m i a l if it has exactly one term. It is called b i n o m i a l if it has exactly two non-zero terms. A polynomial ?is a t r i n o m i a l if it has exactly three non-zero terms.
i   The polynomial x +y has exactly two non zero terms , i.e., ? x and y. Therefore, it is a binomial.
ii  The polynomial 1000 has exactly one term, i.e., 1000. Therefore, it is a monomial.
iii The polynomial x +x
2
+x
3
+x
4
 has exactly four terms, i.e., ? x, x
2
, x
3
 and x
4
. Therefore, it doesn't belong to any of the categories.
iv The polynomial 7 +a +5b has exactly three terms, i.e., 7, a and 5b. Therefore, it is a trinomial.
v  The polynomial 2b -3b
2
 has exactly two terms, i.e., ? 2b and -3b
2
. Therefore, it is a binomial.
vi The polynomial 2y -3y
2
+4y
3
 has exactly three terms, i.e., ? 2y, -3y
2
 and 4y
3
. Therefore, it is a trinomial.
vii The polynomial 5x -4y +3x has exactly three terms, i.e., ? 5x, -4y and 3x. Therefore, it is a trinomial.
viii The polynomial 4a -15a
2
 has exactly two terms, i.e., 4a and -15a
2
. Therefore, it is a binomial.
ix The polynomial xy +yz +zt +tx has exactly four terms xy, yz, zt and tx. Therefore, it doesn't belong to any of the categories.
x The polynomial pqr has exactly one term, i.e., pqr. Therefore, it is a monomial.
xi The polynomial p
2
q +pq
2
 has exactly two terms, i.e., ? p
2
q and pq
2
. Therefore, it is a binomial.
xi The polynomial 2p +2q has two terms, i.e., ? 2p and 2q. Therefore, it is a binomial.