## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Ex 10.1

Question 1.

Identify the terms, their numerical as well as literal coefficients in each of the following expressions:

(i) 12x^{2}yz – 4xy^{2}

(ii) 8 + mn + nl – lm

Solution:

Question 2.

Identify monomials, binomials, and trinomials from the following algebraic expressions :

(i) 5p × q × r^{2}

(ii) 3x^{2} + y ÷ 2z

(iii) -3 + 7x^{2}

(iv) \(\frac{5 a^{2}-3 b^{2}+c}{2}\)

(v) 7x^{5} – \(\frac{3 x}{y}\)

(vi) 5p ÷ 3q – 3p^{2} × q^{2}

Solution:

Question 3.

Identify which of the following expressions are polynomials. If so, write their degrees.

(i) \(\frac{2}{5}\)x^{4} – \(\sqrt{3}\)x^{2} + 5x – 1

(ii) 7x^{3} – \(\frac{3}{x^{2}}\) + \(\sqrt{5}\)

(iii) 4a^{3}b^{2} – 3ab^{4} + 5ab + \(\frac{2}{3}\)

(iv) 2x^{2}y – \(\frac{3}{x y}\) + 5y^{3} + \(\sqrt{3}\)

Solution:

Question 4.

Add the following expressions:

(i) ab – bv, bv – ca, ca – ab

(ii) 5p^{2}q^{2} + 4pq + 7,3 + 9pq – 2p^{2}q

(iii) l^{2} + m^{2} + n^{2}, lm + mn, mn + nl, nl + lm

(iv) 4x^{3} – 7x^{2} + 9, 3x^{2} – 5x + 4, 7x^{3} – 11x + 1, 6x^{2} – 13x

Solution:

Question 5.

Subtract:

(i) 8a + 3ab – 2b + 7 from 14a – 5ab + 7b – 5

(ii) 8xy + 4yz + 5zx from 12xy – 3yz – 4zx + 5xyz

(iii) 4p^{2}q – 3pq + 5pq^{2} – 8p + 7q -10 from 18 – 3p – 11q + 5pq – 2pq^{2} + 5p^{2}q

Solution:

Question 6.

Subtract the sum of 3x^{2} + 5xy + 7y^{2} + 3 and 2x^{2} – 4xy – 3y^{2} + 7 from 9x^{2} – 8xy + 11y^{2}

Solution:

Question 7.

What must be subtracted from 3a^{2} – 5ab – 2b^{2} – 3 to get 5a^{2} – 7ab – 3b^{2} + 3a ?

Solution:

Question 8.

The perimeter of a triangle is 7p^{2} – 5p + 11 and two of its sides are p^{2} + 2p – 1 and 3p^{2} – 6p + 3. Find the third side of the triangle.

Solution: