Exercise 9.1
Question 1: Identify the terms, their coefficients for each of the following expressions:
[i] 5xyz2 - 3zy
[ii] 1 +x+ x2
(iii) 4x2y2 - 4x2y2z2 + z2
[iv] 3 - pq + qr — rp
(v) x/2 + y/2 - xy
[vi] 0.3a - 0.6ab + 0 5b
Answer 1:
(i)
Terms: 5xyz2 - 3zy
Coefficient in x is 5 and in -3zy is -3
(ii)
Terms: 1 +x+ x2
Coefficient of x and coefficient of x2 is 1.
(iii)
Terms: 4x2y2 - 4x2y2z2 + z2
Coefficient in 4x2y2 is 4, coefficient of -4x2y2z2 is -4 and coefficient of z2 is 1.
[iv]
Terms: 3 - pq + qr — rp
Coefficient of -pq is -1, coefficient of qr is 1 and coefficient of -rp is -1.
[v]
Terms : x/2 , y/2 , -xy
Coefficient of x/2 is 1/2, coefficient of y/2 is 1/2 and coefficient of -xy is -1.
[vi]
Terms: 0.3a,-0.6ab and 0.56
Coefficient of 0.3a is 0.3, coefficient of -0.6ab is -0.6 and coefficient of 0.5b is 0.5
Question 2:
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories:
Answer 2:
Question 3:
Add the following:
Answer 3:
Question 4:
(a) Subtract 4a-7zb + 3b + 12 from 12a-9ab+5b-3
(b) Subtract 3xy + 5yz - 7zx from 5xy - 2yz - 2zx + 10 xyz
(c) Subtract 4p2q - 3pq + 5pq2 - 8p + 7q - 10 from 18- 3p-11q+5pq-2qp2 + 5 p2q
Answer 4:
(a)
(b)
(c)
Exercise 9.2
Question 1:
Find the product of the following pairs of monomials:
(i) 4, 7p
(ii) -4p, 7p
(iii) - 4p, 7pq
(iv) 4p3, - 3p
(v) 4p, 0
Answer 1:
Question 2:
Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively:
(p,q); (10m,5n); (20x2,5y2); (4x,3x2); (3mn,4np)
Answer 2:
[i] Area of rectangle = length x breadth
= pxq = pq sq. units
[ii] Area of rectangle = length x breadth
= 10m x 5n = (10x5)(mxn) = 50 mn sq. units
[iii] Area of rectangle = length x breadth
= 20x2 x 5y2 = (20 x 5 ) (x2 x y2) = 100x2y2 sq. units
(iv) Area of rectangle = length x breadth
= 4x x 3x2 = (4x3)(x x x2 ) sq. units
(v) Area of rectangle = length x breadth
= 3mn x 4np = (3x4)(mn x np) = 12mn2p sq. units
Question 3:
Complete the table of products:
First monomial → Second monomial | 2x | —5y | 3x2 | -4 xy | 7x2y | -9 x2y2 |
2x | 4x2 | ..... | ..... | ..... | ..... | ..... |
-5y | ..... | ..... | -15x2y | ..... | ..... | ..... |
3x2 | ..... | ..... | ..... | ..... | ..... | ..... |
-4 xy | ..... | ..... | ..... | ..... | ..... | ..... |
7x2y | ..... | ..... | ..... | ..... | ..... | ..... |
-9x2y2 | ..... | ..... | ..... | ..... | ..... | ..... |
Answer 3:
First monomial → Second monomial | 2x | —5y | 3x2 | -4 xy | 7x2y | -9 x2y2 |
2x | 4x2 | -10xy | 6x3 | -8x2y | 14x3y | -18x3y2 |
-5y | -10xy | 25 y2 | -15x2y | 20 xy2 | -35x2y2 | -45 x2y3 |
3x2 | 6x3 | -15x2y | 9x4 | -12x3y | 21 x4y | -27 x4y2 |
-4 xy | 8x2y | 20 xy2 | -12x3y | 16x2y2 | -28 x3y2 | 36 x3y3 |
7x2y | 14x3y | -35 x2y2 | 21 x4y | -28x3y2 | 49 x4y2 | -63 x4y3 |
-9x2y2 | -18x3y2 | 45x2y3 | -27 x4y2 | 36 x3y3 | -63x4y3 | 81 x4y4 |
Question 4:
Obtain the volume of rectangular boxes with the following length, breadth and height respectively:
(i) 5a, 3a27a4
(ii) 2p,4q18r
(iii) xy, 2x2y, 2xy2
(iv) a, 2b, 3c
Answer 4:
(i) Volume of rectangular box = length x breadth x height
= 5a x 3 a2 x 7a4 = ( 5x3x7)(a x a2 x a4)
= I05a7 cubic units
(ii) Volume of rectangular box = length x breadth x height
= 2p x 4 q x 8r = ( 2x4x8)(pxqxr)
= 64 pqr cubic units
(iii) Volume of rectangular box = length x breadth x height
= xy, 2x2y, 2xy2 = (1 x 2 x 2 )(x x x2 x yx yx y2)
= 4x4 y2 cubic units
(iv)
Volume of rectangular box = length x breadth x height
= a x 2b x 3c = (1x2x3) (axbxc) 6abc cubic units
Question 5:
Obtain the product of:
(i) xy,yz,zx
(ii) a, -a2, a3
(iii) 2, 4y, 8y2, 16y3
(iv) a,2b,3c,6abc
(v) m, -mn,mnp
Answer 5:
Exercise 9.3
Question 1:
Carry out the multiplication of the expressions in each of the following pairs:
(i) 4p,q+r
(ii) ab, a-b
(iii) a+ b, 7a2b2
(iv) a2- 9, 4a
(v) pq+qr+rp,0
Answer 1:
Question 2:
Complete the table:
Answer 2:
Question 3:
Find the product:
Answer 3:
Question 4:
(a) Simplify:
Answer 4:
Question 5:
Answer 5:
1. What are algebraic expressions? |
2. How do you simplify algebraic expressions? |
3. What is the difference between an equation and an expression? |
4. How do you evaluate algebraic expressions? |
5. What are the applications of algebraic expressions in real life? |
|
Explore Courses for Class 8 exam
|