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Q1. Classify the following as monomial, binomial or trinomial: (i) 2x + 3y (ii) 2x³ + 3y² - 1 (iii) 2xy + 10 (iv) -9x⁴yz

Solution

(i) 2x + 3y : Binomial (ii) 2x³ + 3y² - 1 : Trinomial (iii) 2xy + 10 : Binomial (iv) -9x⁴yz : Monomial

Q2. Identify like terms in the followings: -xy², -7yx², -6x²z², -18z²x², 3x²y, 2xy²

Solution

-xy² and 2xy² are like terms. -7yx² and 3x²y are like terms. -6x²z² and -18z²x² are like terms.

Q3. An electrician charges Rs 45 per hour and spends Rs 20 a day on gasoline. Write an algebraic expression to represent his earnings for one day.

Solution

Let x represent the number of hours the electrician works in one day. Since charges is Rs 45 per hours. So the charges for x hours is RS 45x. Now Rs 20 is spend on gasoline, therefore The electrician's earning can be represented by the following algebraic expression 45x - 20

Q4. Add the following expressions: 6m - 7n - 5p, -4m - 9n + 6p, -4m - 9n + 6p

Solution

Required sum: (6m - 7n - 5p) + (-4m - 9n + 6p) + (-4m - 9n + 6p) = 6m - 7n - 5p - 4m - 9n + 6p - 4m - 9n + 6p = (6m - 4m - 4m) + (-7n - 9n - 9n) + (-5p + 6p + 6p) = (6 - 4 - 4)m + (-7 - 9 - 9)n + (-5 + 6 + 6)p = -2m - 25n + 7p

Q5. From the sum of 3x - y + z and -y - z, subtract 3x - y - z.

Solution

We have to find:[(3x - y + z) + (-y - z)] - (3x - y - z) = [3x - y + z - y - z] - (3x - y - z) = (3x - 2y) - (3x - y - z) = 3x - 2y - 3x + y + z = 3x - 3x - 2y + y + z = -y + z

Q6. Add: 4x + 6 and 3x - 7.

Solution

We have to find: (4x + 6) + (3x - 7) = 4x + 6 + 3x - 7 = (4x + 3x) + (6 - 7) = 7x - 1

Q7. Express each of the following as an algebraic expression. (a) Sum of y and 7. (b) Number a divided by 23.

Solution

(a) y + 7(b) a/23

Q8. Write the following in product form: (i) (3q)⁵(ii) 3q⁵(iii) 3⁵q

Solution

(i) (3q)⁵ = 3q x 3q x 3q x 3q x 3q (ii) 3q⁵ = 3 x q x q x q x q x q (iii) 3⁵q = 3 x 3 x 3 x 3 x 3 x q

Q9. Define monomial, binomial and trinomial and two examples of each.

Solution

Monomial: An algebraic expression consisting only one term is called a monomial. Examples: x²y, -5xy² Binomial: An algebraic expression consisting two terms is called a binomial. Examples: y - 7x², -6 + x² Trinomial: An algebraic expression consisting three terms is called a trinomial. Examples: 1 + x + x², -1 + z² - z²x², 3x + 2y - z

Q10. Write the following in exponent form: (i) -5 x a x a x a x b x b x b x b (ii) -2 x 3 x 3 x a x a x b x b x b x c

Solution

(i) -5 x a x a x a x b x b x b x b = -5x a³ x b⁴ = -5a³b⁴ (ii) -2 x 3 x 3 x a x a x b x b x b x c = -2 x 3² x a² x b³ x c = -18a²b³c