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(i) \(5xyz^2 – 3zy\)

(ii) \(1 + x + x^2\)

(iii) \(4x^2y^2 – 4x^2y^2z^2 + z^2\)

(iv) \(3 – pq + qr -rp\)

(v) \(\frac { x }{ 2 } +\frac { y }{ 2 } -xy\)

(vi)\( 0.3a – 0.6ab + 0.5b\)

Answer :

(i) We have 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)We have the expression \(1 + x + x^2\), the terms are 1, x and \(x^2\).

Coefficient of the 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) We have the expression \(4xy – 4xyz + z\) , the terms are \(4x^2y^2, – 4x^2y^2z^2\) and \(z^2\).

Coefficient of \(x^2y^2\) in the term \(4x^2y^2\) is 4.

Coefficient of \(x^2y^2z^2\) in the term \(– 4x^2y^2z^2\) is – 4.

Coefficient of \(z^2\) in the term \(z^2\) is 1.

(iv) We have the expression \(3 – pq + qr – rp\), the terms are 3, – pq, qr and – rp.

Coefficient of the 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) We have the expression \(\frac { x }{ 2 } +\frac { y }{ 2 } -xy\), the terms are \(\frac { x }{ 2 } ,\frac { 7 }{ 2 }\) and \(– xy\).

Coefficient of x in the term \(\frac { x }{ 2 }\) is \(\frac { 1 }{ 2 }\)

Coefficient of y in the term \(\frac { y }{ 2 }\) is \(\frac { 1 }{ 2 }\)

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.

- 2.Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories? \(x + y, 1000, x + x^2 + x^3 + x^4, 7 + y + 5x, 2y – 3y^2, 2y – 3y^2 + 4y^3\),\( 5x – 4y + 3xy, 4z – 15z^2, ab + bc+cd + da, pqr, p^2q + pq^2, 2p + 2q.\)
- 3.Add the following : (i) \(ab – be, be – ca, ea – ab\) (ii)\( a – b + ab, b-c + be, c – a + ac\) (iii) \(2p^2q^2 – 3pq + 4, 5 + 7pq – 3p^2q^2\) (iv)\( l^2 + m^2, m^2 + n^2, n^2 + l^2, 2lm + 2mn + 2nl\)
- 4.(a) Subtract \(4a – 7ab + 3b + 12\) from \(12a – 9ab + 5b – 3\) (b) Subtract \(3xy + 5yz – 7zx\) from \(5xy – 2yz – 2zx + 10xyz\) (c) Subtract \(4p^2q – 3pq + 5pq^2 – 8p + 7q – 10 \) from \(18 – 3p – 11q + 5pq – 2pq^2 + 5p^2q\)
- 4.Obtain the volume of rectangular boxes with the following length, breadth and height respectively. (i) \(5a, 3a^2, 7a^4\) (ii) \(2p, 4q, 8r\) (iii) \(xy, 2x^2y, 2xy^2\) (iv) \(a, 2b, 3c\)

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