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

(i) 7p² × a³b

(ii) 5 + 3x³y³z²

(iii) 3x² ÷ p

(iv) $\dfrac{3a + 2b - 5c}{7}$

(v) xy + yz - zx

(vi) ax² + bx × y²

Write down the numerical as well as literal coefficient of each of the following monomials:

(i) -2p³q²

(ii) $\dfrac{5}{9}xyz^2$

(iii) $-\dfrac{3ab^2}{2}$

(iv) $\dfrac{3}{a^2}$

(v) $\dfrac{2ab}{c}$

(vi) $-\dfrac{2x^2}{yz}$

Identify like terms in the following:

(i) a², b², -2a², c², 4a

(ii) 3x, 4xy, -yz, $\dfrac{1}{2}$zy

(iii) -2xy², x²y, 5y²x, x²z

(iv) abc, ab²c, acb², c²ab, b²ac, a²bc, cab²

Generate algebraic expressions for the following:

(i) The product of a and b added to their sum.

(ii) The quotient of x by 8 is multiplied by y.

(iii) Thrice x added to y squared.

(iv) One-third of x multiplied by the sum of p and q.

(v) The number to be added to x + y to make it equal to p.

(vi) From a rod (p + q) units in length, n equal pieces are cut. Find the length of each piece.

(vii) Five times m subtracted from the sum of p and thrice x.

(viii) The number obtained when m times the difference of x and y is subtracted from n times the sum of x and y.

(ix) The sum of 7 numbers each equal to p.

(x) The product of three numbers a, b and c subtracted from the sum of x and y.