Question 1.
Identify the terms, their coefficients for each of the following expressions:
Question 2.
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?
Solution.
Question 3.
Add the following.
- (i) ab – be, be – ca, ca – ab
- (ii) a -b + ab, b – c + be, c – a + ac
Question 4.
- (a) Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 56 – 3
- (b) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz
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.
Solution.
Question 2.
Find the areas of rectangles with the following pairs of mononials as their lengths and breadths respectively:
Solution.
(i) (p, q)
Length = p
Breadth = q
∴ Area of the rectangle
= Length x Breadth
= pxq
= pq
(ii) (10m, 5n)
Length = 10 m
Breadth = 5 n
∴ Area of the rectangle
= Length x Breadth
= (10m) x (5n)
= (10 x 5) x (m x n)
= 50 x (mn)
= 50 mn
= 12×3
(v) (3mn, 4np)
Length = 3 mn
Breadth = 4np
∴ Area of the rectangle
= Length x Breadth
= (3mn) x (4np)
= (3 x 4) x (mn) x (np)
= 12 x m x (n x n) x p
= 12mn2p
Question 3.
Complete the table of products.
Solution
Question 4.
Obtain the volume of rectangular boxes with the following length, breadth and height respectively:
(ii)2p,4q,8r
(iv) a, 2b, 3c
Question 5.
Obtain the product of
(v) m, – mn, mnp
Question 1.
Carry out the multiplication of the expressions in each of the following pairs:
Solution.
Question 2.
Complete the table
Solution.
Question 3.
Find the product:
Solution.
Question 4.
- (a) Simplify: 3x (4x – 5) + 3 and find its values for (i) x = 3, (ii) x=12
- (b) Simplify: a(a2+a+1)+5 and find its value for (i)a = 0, (ii)a = 1 and (iii) a = -1.
Solution.
Question 5.
- (a) Add: p(p – q), q(q – r) and r(r -p)
- (b) Add: 2x(z – x – y) and 2y (z – y – x)
- (c) Subtract: 3l (l – 4m + 5n) from 4l (10n – 3m + 2l)
- (d) Subtract: 3a(a + b + c) – 2b(a – b + c) from 4c(- a + b + c).
Solution.
Question 1.
Multiply the binomials:
- (i) (2x + 5) and (4x – 3)
- (ii) (y – 8) and (3y – 4)
- (iii) (2.5l – 0.5 m) and (2.5l + 0.5m)
- (iv) (a + 3b) and (x + 5)
Solution.
Question 2.
Find the product:
- (i) (5 – 2x) (3 + x)
- (ii) (x + 7y) (7x —y)
Solution.
Question 3.
Simplify.
Solution.
Question 1.
Use a suitable identity to get each of the following products:
Solution
Solution.
Question 3.
Find the following squares by using the identities.
Solution.
Question 4.
Simplify:
Solution.
Question 5.
Show that:
Solution.
Question 6.
Using identities, evaluate:
Solution.
Question 7.
Using a2−b2=(a+b)(a−b), find
Solution.
Question 8.
Using (x+a)(x+b)=x2+(a+b)x+ab, find
- (i) 103 x 104
- (ii) 5.1 x 5.2
- (iii) 103 x 98
- (iv) 9.7 x 9.8
Solution.
