Exercise 10.1

1. Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

(i) Subtraction of z from y : y - zy x zy + z

(ii) One-half of the sum of numbers x and y : (1/2)(x+y)(1/2)(x-y)(1/4)(x+y)

(iii) The number z multiplied by itself : z × zz - zz + z

(iv) One-fourth of the product of numbers p and q : (1/4)pq(1/2)p + q(1/4)p - q

(v) Numbers x and y both squared and added : (x × y)(y × y)(x + y)(x × y)

(vi) Number 5 added to three times the product of numbers m and n : 5 + 3mn5 - 3m5 + mn

(vii) Product of numbers y and z subtracted from 10 : 10 - yz10 + yz10y - z

(viii) Sum of numbers a and b subtracted from their product : ab - (a+b)a - b - (ab)ab + ab

2. (i) Identify the terms and their factors in the following expressions show the terms and factors by tree diagrams.

(a) x – 3

(b) 1 + x + x2

(c) y - y3

(d) 5xy2 + 7x2y

(e)– ab + 2b2 – 3a2

(ii) Identify terms and factors in the expressions given below.

3. Identify the numerical coefficients of terms (other than constants) in the following expressions

(i)5 - 3t2

is the coefficient of t2

(ii)1 + t + t2 + t3

, 1 , are the coefficients of t , t2 , t3

(iii)x + 2xy + 3y

, , are the coefficients of x, xy and y

(iv)100m + 1000m

and are the coefficients of m and n

(v)-p2q2+7pq

and are the coefficients of p2q2 and pq

(vi)1.2a + 0.8b

and are the coefficients of a and b

(vii)3.14r2

is the coefficient of r2

(viii)2(l+b)

and are the coefficients of l and b

(ix)0.1y + 0.01y2

and are the coefficients of y and y2

4. (a) Identify terms which contain x and give the coefficient of x.

(i)y2x+y

Term containing x = y2xy3 and Coefficient of x = y2xy

(ii)13y2 - 8yx

Term containing x = -8yx8xy and Coefficient of x = -8y-8y

(iii)x + y + 2

Term containing x = xy2 and Coefficient of x = 102

(iv)5 + z + zx

Term containing x = zxz+xxz and Coefficient of x = zx

(v)1 + x + xy

Term containing x = xy; xyx+y and Coefficient of x in both the terms = ,

(vi)12xy2 + 25

Term containing x = 12xy2xy2 and Coefficient of x = 12y2y2

(vii)7x + xy2

Term containing x = 7xx; xy2xy and Coefficient of x in both the terms = ,y2x2

(b) Identify terms which contain y2 and give the coefficient of y2.

(i) 8 - xy2

Term containing y2 = -xy2-xy and Coefficient of y2 = -xx-y

(ii)5y2 + 7x

Term containing y2 = 5y2y5 and Coefficient of y2 =

(iii)2x2y - 15xy2 + 7y2

Term containing y2 = -15xy215y2 ; 7y27x2 and Coefficient of y2 in both the terms = -15x15x ,

5. Classify into monomials, binomials and trinomials.

Instruction

6. State whether a given pair of terms is of like or unlike terms.

Instruction

7. Identify like terms in the following.

(a)

Instruction

(b)