Page 140 - ICSE Math 8

5. Write the coefficient of the following.
4
4 2
3
2
2 2 2
(a) y in 7y 3 (b) x in 8x y (c) xyz in x y z (d) 7y in 7y 3
3
x x yz
2
2
2
3
2
(e) –b in –3 – 2ab (f) 4xy in x –4xy + x (g) 7 in 49 (h) yz in 12xy z
6. Which of the following algebraic expressions are polynomials? If so, find their degree.
1 11xy x 7 5
4
4
2
3
(a) x + 2 (b) y – 5y + y (c) 7x + 13 + 5 (d) z – + z 3
z
x
7. Write the degree of each of the following polynomials.
2
2
7
3
(a) yz + 7z (b) 5x + 6x – 2 (c) x y + 29 (d) y + x y
8. Separate the following into groups of like terms.
7
2 2
2 2
3 3
2 2
3 3
24xyz, 13a b , 2a b , –9a b , –13yzx, 24b a , 13 a b
Addition and Subtraction of Algebraic Expressions
To add or subtract two or more algebraic expressions, the numerical coefficients of the like terms are added
or subtracted using the laws of addition of integers.
Addition and subtraction of like terms
The sum or difference of two or more like terms is a like term whose numerical coefficient is the sum or
difference of the numerical coefficients of the given terms. For example,
(a) 3a + 7a = (3 + 7)a = 10a (b) 6xy – 2xy = (6 –2)xy = 4xy
2  2  − 7
52 xy =
(c) xy − 5xy + 2xy =  −+  xy
3  3  3
Addition and subtraction of unlike terms
Two unlike terms can never be added or subtracted to form a single term. So, we just write the unlike terms as
the terms of the algebraic expression with an appropriate sign. For example, the sum of 5xy and 3ab is
5xy + 3ab and the difference of 2ab from 6xy is 6xy – 2ab.

Addition of polynomials
Horizontal method
1. Arrange the like terms together and add.
2. Write the unlike terms as terms of the algebraic expression.
Column method
1. Write the polynomials to be added one below the other such that the like terms (with signs) lie in the same
vertical column.
2. Add column wise.
Example 3: Add 3x + 4y – 5z, 4x + 6y + 3z and 2x – 7y + 4z. Alternatively,
Solution: (3x + 4y – 5z) + (4x + 6y + 3z) + (2x – 7y + 4z) by column method:
= (3x + 4x + 2x) + (4y + 6y – 7y) + (–5z + 3z + 4z) 3x + 4y – 5z

= (3 + 4 + 2)x + (4 + 6 – 7)y + (–5 + 3 + 4)z 4x + 6y + 3z
= 9x + 3y + 2z 2x – 7y + 4z
9x + 3y + 2z

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