Page 48 - SM inner class 8.cdr

Example 2. Add: 6a + 8b - 7c, 2b + c - 4a and 2. Subtraction of Algebraic Expression
a - 3 b - 2 c
Rule for subtraction: Change the sign of each
Solution: Writing the terms of the given
term of the expression to be subtracted and
expressions in the same order in form of rows add it to the expression from which
with like terms below each other and adding
subtraction is to be made.
column wise;
2
6a + 8b - 7c Example 4. Subtract 2x - 3x - 5 from
2
3
x - x + 7
- 4a + 2b + c
Solution:
a - 3b - 2c
3
x - x 2 + 7
3a + 7b - 8c
– -3x 2 + 2x - 5
\ Sum is = 3a + 7b - 8c + - +
3
2
Example 3. Find the sum of the following two x + 2 x - 2 x + 12
polynomials: Changing sign and Adding
5
3
3
5
4
(3y - 2y + y + 2y + ) 5 and (2y + 3y + 2 + 7y ) Example 5. Subtract 4a + 5b - 3c from
4
3
5
(1) Write in Standard form (3y + y + 2y 6a - 3b + c
2
- 2y + 5) + (2y 5 + 3y 3 + 7y + ) Solution:
(ii) Arrange in columns of like terms and then 6a - 3b + c
add – + 4a + 5b - 3c
-
4
3
+
-
5
3y + y + 2y - 2y + 5 ( ) ( ) ( )
3
2y 5 + 3y + 7y + 2 2a - 8b + 4c
3
5
4
5y + y + 5y + 5y + 7
E xercise 6.1
2
2
2
2
-
y
1. Add: 5x + 7y - 8 4y + 7 2x and 6 5 + 4x – 5y + 4x .
,
-
2
2
2
2
2
2
x
-
2. Add: 8x - 5xy + 3y , 2xy - 6y + 3x and y + xy 6 .
2
3
2
3. Add these expres sion: x - x + 7, -9x +10x 2 -6 and 2x - 3x - 5
4. Subtract 3x + - 3z from 9x - 5y + z
y
2
2
5. Subtract 9a - 3a from 6a - 10a .
2
2
6. Subtract 3x - 6x - 4 from 5 + - 2x .
x
2
2
3
3
7. Subtract a - a 4 2 + a 5 - 6 from the sum of 3a + a + 1 and a - 2.
3
2
8. What should be subtracted from a - a 4 2 + a 5 - 6 to obtain a - a 2 + 1.
Multiplication of Algebraic Expressions 4. Multiplication of Polynomial by Binomial
In arithmetic only positive numbers are used.
1. Multiplication of monomial by
But in algebra, besides positive numbers,
monomial
negative numbers and literal numbers are used.
For this we need to have a clear understanding Steps used in multiplication of monomial by
of few points while multiplication. monomial:
There are different types of multiplication. Step 1: Multiply the numerical
coefficients of the monomials
1. Multiplication of Monomial by Monomial
along with their signs and write
2. Multiplication of Monomial by Binomial the product.
3. Multiplication of Polynomial by Monomial
48
Mathematics In Focus - 8