**Algebraic Expressions and Identities**

**Question 1.****Identify the terms, their coefficients for each of the following expressions :(i)** 5xyz

^{2}– 3zy

**(ii)**1 + x + x

^{2}

**(iii)**4x

^{2}y

^{2}– 4x

^{2}y

^{2}z

^{2}+ z

^{2}

**(iv)**3 – pq + qr -rp

**(v)**

**(vi)**0.3a – 0.6ab + 0.5b

**Solution:****(i)** In the expression 5xyz^{2} – 3zy, the terms are 5xyz^{2} and -3zy.

Coefficient of xyz^{2} in the term 5xyz^{2} is 5.

Coefficient of zy in the term – 3yz is – 3.

**(ii)** In the expression 1 + x + x^{2}, the terms are 1, x and x^{2}.

Coefficient of term 1 is 1.

Coefficient of x in the term x is 1.

Coefficient of x^{2} in the term x^{2} is 1.

**(iii)** In the expression 4x y – 4xyz + z , the terms are 4x^{2}y^{2}, – 4x^{2}y^{2}z^{2} and z^{2}.

Coefficient of x^{2}y^{2} in the term 4x^{2}y^{2} is 4.

Coefficient of x^{2}y^{2}z^{2} in the term – 4x^{2}y^{2}z^{2} is – 4.

Coefficient of z^{2} in the term z2 is 1.

**(iv)** In the expression 3 – pq + qr – rp, the terms are 3, – pq, qr and – rp.

Coefficient of term 3 is 3.

Coefficient of pq in the term – pq is -1.

Coefficient of qr in the term qr is 1.

Coefficient of rp in the term – rp is -1.

**(v)** In the expression , the terms are and – xy.

Coefficient of x in the term is

Coefficient of y in the term is

Coefficient of xy in the term – xy is -1.

**(vi)** In the expression 0.3a -0.6 ab + 0.5 b, the terms are 0.3a, – 006ab and 0.5b.

Coefficient of a in the term 0.3a is 0.3.

Coefficient of ab in the term – 0.6ab is – 0.6.

Coefficient of b in the term 0.5b is 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 + x

^{2}+ x

^{3}+ x

^{4}, 7 + y + 5x, 2y – 3y

^{2}, 2y – 3y

^{2}+ 4y

^{3}, 5x – 4y + 3xy, 4z – 15z2, ab + bc+cd + da, pqr, p

^{2}q + pq

^{2}, 2p + 2q.

**Solution:**

The given polynomials are classified as under :

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 + 3x.

Polynomials that do not fit in any categories :

x + x^{2} + x^{3} + x^{4}, ab + be + cd + da.

**Question 3.****Add the following :(i)** ab – be, be – ca, ea – ab

**(ii)**a – b + ab, b-c + be, 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}, 2Im + 2mn + 2nl

**Solution:****(i)** Writing the given expressions in separate rows with like terms one below the other, we have

**(ii)** Writing the given expressions in separate rows with like terms one below the other, we have

**(iii)** Writing the given expressions in separate rows with like terms one below the other, we have

**(iv)** Writing the given expressions in separate rows with like terms one below the other, we have

**Question 4.****(a)** **Subtract** 4a – lab +36 + 12 from 12a – 9a6 + 56-3

**(b)** **Subtract** 3xy + 5yz – Izx from 5xy – 2yz – 2zx + IQxyz

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

**Solution:**

Rearranging the terms of the given expressions, changing the sign of each term of the expression to be subtracted and adding the two expressions, we get