**NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1 – Algebraic Expressions & Identities**

**NCERT Solutions for Class 8 Maths Chapter 9 Exercise 9.1 – Algebraic Expressions & Identities, has been designed by the NCERT to test the knowledge of the student on the following topics:-**

- What are Expressions?
- Terms, Factors and Coefficients
- Monomials, Binomials and Polynomials
- Like and Unlike Terms
- Addition and Subtraction of Algebraic Expressions

**Q.1 Identify the terms, their coefficients for each of the following expressions.**

**(i) 5****xyz**^{2}** − 3****zy**

(ii) 1 + **x**** + ****x**^{2}

(iii) 4**x**^{2}**y**^{2}** − 4****x**^{2}**y**^{2}**z**^{2}** + ****z**^{2
}**(iv) 3 − ****pq**** + ****qr**** − ****rp**

(v) x/2 +y/2 – xy

(vi) 0.3**a**** − 0.6****ab**** + 0.5****b**

**Solution:**

The terms and their coefficients of the given expressions:

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

**x + y, 1000, x + x ^{2} + x^{3} + x^{4}, 7 + y + 5x, 2y − 3y^{2}, 2y − 3y^{2} + 4y^{3}, 5x − 4y + 3xy, 4z − 15z^{2}, ab + bc + cd + da, pqr, p^{2}q + pq^{2}, 2p + 2q**

**Solution: **

The given polynomials are classified as

**Monomials:** 1000, pqr

**Binomials:** x + y, 2y − 3y^{2}, 4z − 15z^{2}, p^{2}q + pq^{2}, 2p + 2q

**Trinomials:** 7 + y + 5x, 2y − 3y^{2} + 4y^{3}, 5x − 4y + 3xy

**Polynomials that do not fit in any of these categories: **x + x^{2} + x^{3} + x^{4} , ab + bc + cd + da

**Q.3 Add the following. **

**(i) ab − bc, bc − ca, ca − ab
**

**(ii) a − b + ab, b − c + bc, c − a + ac**

**(iii) 2p**

^{2}q^{2}− 3pq + 4, 5 + 7pq – 3p^{2}q^{2}**(iv) l**

^{2}+ m^{2}, m^{2}+ n^{2}, n^{2}+ l^{2}, 2lm + 2mn + 2nl**Solution: **

Writing the expressions in separate rows, with like terms one below the other, we have

**(i) **

Therefore, sum of the given expressions is 0

**(ii) **

Therefore, sum of the given expressions is ab + bc + ac

**(iii) **

Therefore, sum of the given expressions is −p^{2}q^{2} + 4pq + 9

**(iv) **

Therefore, sum of the given expressions is 2(l^{2} + m^{2 }+ n^{2 }+ lm + mn + nl).

**Q.4 **

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

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

**(c) Subtract 4p ^{2}q − 3pq + 5pq^{2} − 8p + 7q − 10 from 18 − 3p − 11q + 5pq − 2pq^{2} + 5p^{2}q **

**Solution: **

Writing the expressions in separate rows, with like terms one below the other, we have

**(a) **

**(b) **

**(c)**

**The next Exercise for** **NCERT Solutions for Class 8 Maths Chapter 9 Exercise 9.2 – Algebraic Expressions and Identities can be accessed by clicking here**

**NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1 – Algebraic Expressions & Identities**

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