Q1. Identify the terms, their coefficients for each of the following expressions.

(i)5xyz² – 3zy

(ii) 1 + x + x²

(iii) 4x²y2 – 4x²y²z² + z²

(iv) 3 – pq + qr – p

(v) (x/2) + (y/2) – xy

(vi) 0.3a – 0.6ab + 0.5b

Solution:

Sl. No.	Expression	Term	Coefficient
i)	5xyz2 – 3zy	5xyz2  -3zy	5, -3
ii)	1 + x + x2	1  x  x2	1, 1, 1
iii)	4x2 y2  – 4x2 y2 z2 + z2	4x2 y2 -4 x2 y2 z2 z2	4, -4, 1
iv)	3 – pq + qr – p	3 -pq qr -p	3, -1, 1, -1
v)	(x/2) + (y/2) – xy	x/2 Y/2 -xy	½ ,1/2, -1
vi)	0.3a – 0.6ab + 0.5b	0.3a -0.6ab 0.5b	0.3 ,-0.6, 0.5

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, p ² q + pq ² , 2p + 2q

Solution:

Expressions	Category
x + y	Binomial
1000	Monomial
x + x2 + x3 + x4	Polynomial, [it does not fit in listed three categories]
2y – 3y2	Binomial
2y – 3y2 + 4y3	Trinomial
5x – 4y + 3xy	Trinomial
4z – 15z2	Binomial
ab + bc + cd + da	Polynomial, [ it does not fit in listed three categories]
pqr	Monomial
p 2 q + pq 2	Binomial
2p + 2q	Binomial
7 + y + 5x	Trinomial

3.  Add the following.

(i) ab – bc, bc – ca, ca – ab

Solution:

According to question:

= (ab – bc) + (bc – ca) + (ca-ab)

= ab – bc + bc – ca + ca – ab

= ab – ab – bc + bc – ca + ca

= 0

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

Solution:

According to question:

= (a – b + ab) + (b – c + bc) + (c – a + ac)

= a – b + ab + b – c + bc + c – a + ac

= a – a +b – b +c – c + ab + bc + ca

= 0 + 0 + 0 + ab + bc + ca

= ab + bc + ca

(iii) 2p ²q² – 3pq + 4, 5 + 7pq – 3p ² q²

Solution:

According to question:

= 2p ²q² – 3pq + 4, 5 + 7pq – 3p ² q²

= (2p ²q²  – 3pq + 4) + (5 + 7pq – 3p ² q²)

= 2p ²q²   – 3p ² q² – 3pq + 7pq + 4 + 5

= – p ²q²  + 4pq + 9

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

Solution:

According to question:

= (l² + m²) + (m² + n²) + (n²+ l²) + (2lm + 2mn + 2nl)

= l² + l²+ m² + m² + n² + n² + 2lm + 2mn + 2nl

= 2l² + 2m² + 2n² + 2lm + 2mn + 2nl

Thus, the sum of the given expressions is 2(l² + m²+ n² + lm + mn + nl)

4.

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

Solution:

According to question:

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

= 12a – 9ab + 5b – 3 – 4a + 7ab – 3b – 12

= 12a – 4a -9ab + 7ab +5b – 3b -3 -12

= 8a – 2ab + 2b – 15

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

Solution:

According to question:

= (5xy – 2yz – 2zx + 10xyz) – (3xy + 5yz – 7zx)

= 5xy – 2yz – 2zx + 10xyz – 3xy – 5yz + 7zx

=5xy – 3xy – 2yz – 5yz – 2zx + 7zx + 10xyz

= 2xy – 7yz + 5zx + 10xyz

 (c) Subtract 4p²q – 3pq + 5pq² – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq² + 5p²q

Solution:

According to question:

= (18 – 3p – 11q + 5pq – 2pq² + 5p²q) – (4p²q – 3pq + 5pq²– 8p + 7q – 10)

= 18 – 3p – 11q + 5pq – 2pq² + 5p²q – 4p²q + 3pq – 5pq² + 8p – 7q + 10

=18+10 -3p+8p -11q – 7q + 5 pq+ 3pq- 2pq²– 5pq²+ 5 p²q – 4p²q

= 28 + 5p – 18q + 8pq – 7pq² + p² q