Page 123 - Maths Skills - 7

Algebraic Expressions 121

Example 2: Identify the numerical coefficient of each term in the following:

(i) 5x y – 3ab (ii) 4 – 7p (iii) 0.1 y + 0.03 y 2
2
3
Solution: (i) Numerical coefficient of 5x y is 5 and – 3ab is – 3.
2
(ii) Numerical coefficient of 4 is 4 and – 7p is – 7.
3
(iii) Numerical coefficient of 0.1y is 0.1 and 0.03 y is 0.03.
2
Example 3: Identify the like terms in the following:
1
(i) – 6yz, 0.3y , – 8y , – 61zy, 30x y, – y 2
2
2
2
4
1
(ii) – 47ab , 16 pr, – a – 0.07 a, 10 pr, 0.1 pr, 18 a , – 9 ab 2
2
3
2
3
7
Solution: (i) Like terms are: (– 6yz, – 61zy) (ii) Like terms are: (– 47ab , – 0.07 b a, – 9 ab )
2
2
2
1
(16 pr, 10 pr, 0.1 pr)
(0.3y , – 8y , – y )
2
2
2
1
4 (– a , 18a )
3
3
7
Example 4: Write an algebraic expression using variables, constants and arithmetic operators for the following:
(i) Product of two numbers added to their difference.
(ii) A number ‘y’ squared and added to 4x. (iii) Thrice of x subtracted from two times p.
Solution: (i) Let the two numbers be x and y ⇒ xy + (x – y)
(ii) y + 4x (iii) 2p – 3x
2
Example 5: Find the degree of the given polynomials.
(i) a + a + a + 4 (ii) –3a b + 2a b – 5ab + 7 (iii) –7 + x y + x y – xy
3 3
2
2 2
3
2
2
Solution: (i) In descending order of powers the expression is written as
a + a + a + 4
2
3
Here, the highest power is 3. So, the degree of this expression is 3.
(ii) In descending order of their powers, the expression will be
2a b – 3a b – 5ab + 7
2 2
2
Here, the highest power is 4. The degree of this expression is 4.
(iii) In descending order, the expression will be
x y + x y – xy – 7 The degree is 6.
2
3 3
Exercise 7.1

1. Identify the terms and their factors in the following:

(i) 3a – 7b + 6z (ii) – 2a + 5 + 4cd (iii) b – 7t (iv) 9a b – 8ab + 2abc
2
2
2
3
2. Write the algebraic expressions whose terms are:
−1
(i) 3xy, – 4y, 7 (ii) 83xy , ab , 9b, 6 (iii) 8c , – 4b , 19bc, 6a 2
3
2
2
3
7