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# Class 8 NCERT Solutions – Chapter 9 Algebraic Expressions and Identities – Exercise 9.1

• Last Updated : 12 Dec, 2021

### Question 1. Identify the terms, their coefficients for each of the following expressions.

Need to be Known:

• Expression: An Expression is the addition of terms. Example: 7y + z is an expression made up of two terms 7y and z.
• Term: Terms itself is a product of factors. Example: 7y + z, here terms are 7y (term 1) and z (term2) where term 1 is the product of two factors 7 and y . and term 2 is a single factor z.
• Coefficient: It is a numerical factor of the term. Example: 7y + z here term1 has a two factor 7 and y in which 7 is numerical factor hence it is a coefficient.

(i) 5xyz2 – 3zy

Solution:

1. Here terms are 5xyz2 and -3zy
2. Here Coefficients are 5 and -3

(ii) 1 + x + x2

Solution:

1. Here terms are 1, x, x2
2. Here Coefficients are 1, 1, 1

(iii) 4x2y2 – 4x2y2z2 + z2

Solution:

1. Here terms are 4x2y2, –4x2y2z2 and z2
2. Here Coefficients are 4, -4 and 1

(iv) 3 – pq + qr – rp

Solution:

1. Here terms are -3, -pq, qr, -rp
2. Here Coefficients are 3, -1, 1 and -1

(v) x/2 + y/2 – xy

Solution:

1. Here terms are x/2, y/2 and -xy
2. Here Coefficients are 1/2, 1/2 and -1

(vi) 0.3a – 0.6ab + 0.5b

Solution:

1. Here terms are 0.3a, -0.6ab and 0.5b
2. Here Coefficients are 0.3, -0.6 and 0.5

### Question 2. Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?

x + y, 1000,  x + x2 + x3 + x4, 7 + y + 5x, 2y – 3y2,  2y – 3y2 + 4y3,  5x – 4y + 3xy, 4z – 15z2, ab + bc + cd + da,  pqr, p2q + pq2, 2p + 2q

Need to be Known:

• Monomial: Expression made up of one term is known as monomial. Example: pqr, z, ab etc.
• Binomial: Expression made up of two terms is known as binomial. Example: 2y + 3z, 5x – 4y, etc.
• Trinomial: Expression made up of three terms is known as trinomial. Example: 2y + 3z + x, 5x – 4y + a, etc.
• Polynomial: Expression made up of one or more terms is known as a polynomial. Example: a + b + c + d, 3xy, 7xyz – 10, 2x + 3y + 7z, etc

Solution:

In this question:

• Monomials: 1000, pqr
• Binomials: x + y, 2y – 3y2, 4z – 15z2, p2q + pq2, 2p + 2q
• Trinomials: 7 + y + 5x, 2y – 3y2+ 4y3, 5x – 4y + 3xy
• and those which do not fit in these categories are:  x + x2+ x3+ x4, ab + bc + cd + da

### Question 3. Add the following

Need to be Known:

Like term: Terms having the same variable with their same power.

Note**: Terms those are like can only add and subtract each other. unlike terms cannot add and subtract each other. Example: 4x and 5x are like terms as they both have the same coefficient with the same power of x as 1.

Unlike term: Terms having different variable and may have different powers.

1. Example: 4x and 5y are unlike terms as they both have different variables
2. Example: 4x2 and 5x3 are unlike terms as they both terms differ in the variable power.

(i) ab – bc, bc – ca, ca – ab

Solution:

As here three expressions are given, we need to place expressions same terms below other expressions same term one by one then we will get like these:

ab – bc + 0

+    0  + bc  –  ca

+   -ab + 0  + ca

_________________

0  + 0  + 0                     <———-final expression

_________________

this tends to 0.

(ii) a – b + ab, b – c + bc, c – a + ac

Solution:

As here three expressions are given, we need to place expressions same terms below other expressions same term one by one then we will get like these:

a – b + ab

+      0 + b  + 0   – c + bc

+      -a + 0  + 0  + c + 0 + ac

__________________________

0 + 0  + ab + 0 + bc + ac                   <—- final expression

_____________________________

this tends to ab + bc + ac.

(iii) 2p2q2– 3pq + 4, 5 + 7pq – 3p2q2

Solution:

As here two expressions are given, we need to place expressions same terms below other expressions same term one by one then we will get like these:

2p2q2 – 3pq + 4

+  -3p2q2 + 7pq +5

__________________

-1p2q2 + 4pq + 9                <——– final expression

____________________

this tends to -1p2q2 + 4pq + 9.

(iv) l2+ m2, m2 + n2, n2+ l2, 2lm + 2mn + 2nl

Solution:

As here four expressions are given, we need to place expressions same terms below other expressions same term one by one then we will get like these:

l2 + m2

+  0 + m2 + n2

+  l2 + 0   + n2

+  0  + 0 + 0 + 2lm + 2mn + 2nl

_________________________________

2l2 + 2m2 + 2n2 + 2lm + 2mn + 2nl             <———final expression

___________________________________

as 2 is common among all terms then we can take it common this tends to  2( l2 + m2 + n2 + lm + mn + nl)

### Question 4.

(a) Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3

Solution:

Here we need to subtract the given expressions:

then,

12a – 9ab + 5b – 3

(-)     4a – 7ab + 3b + 12

________________________

in subtraction sign of (-) expression gets altered as:

12a – 9ab + 5b – 3

– 4a + 7ab – 3b  – 12

________________________

8a  – 2ab + 2b – 15                  <———final expression

__________________________

this tends to  8a  – 2ab + 2b – 15 .

(b) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz

Solution:

Here we need to subtract the given expressions:

then,

5xy – 2yz – 2zx + 10xyz

(-)  3xy + 5yz – 7zx  + 0

___________________________

in subtraction sign of (-) expression gets altered as:

5xy – 2yz – 2zx + 10xyz

-3xy – 5yz + 7zx  – 0

___________________________

2xy – 7yz + 5zx + 10xyz                       <———– final expression

_____________________________

this tends to 2xy – 7yz + 5zx + 10xyz.

(c) Subtract 4p2q – 3pq + 5pq2– 8p + 7q – 10 from18 – 3p – 11q + 5pq – 2pq2 + 5p2q

Solution:

Here we need to subtract the given expressions:

then,           5p2q + 5pq – 2pq2 – 3p – 11q + 18

(-) 4p2q – 3pq + 5pq2 – 8p + 7q – 10

__________________________________

in subtraction sign of (-) expression gets altered as:

5p2q  + 5pq – 2pq2 – 3p – 11q + 18

-4p2q + 3pq – 5pq2 + 8p – 7q  + 10

__________________________________

p2q + 8pq  – 7pq2 + 5p – 18q + 28              <———–final expression

_____________________________________

this tends to  p2q + 8pq – 7pq2 + 5p – 18q + 28

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