Page 141 - ICSE Math 8

Subtraction of polynomials

Horizontal method
1. Write the polynomial to be subtracted within a bracket with a minus sign preceding it.
2. Remove the bracket and change the sign of each term in the bracket.
3. Combine the like terms and retain the unlike terms.
Column method
1. Write the polynomial to be subtracted below the other polynomial aligning the like terms vertically.

2. Change the sign of each term in the lower row and then combine them column wise.
Example 4: Subtract 4x + 6y + 3z from 7x + 2y – 8z.
Solution: 7 x + 2y – 8z – (4x + 6y + 3z) Alternatively, by column method:

= 7x + 2y – 8z – 4x – 6y – 3z 7x + 2y – 8z
= (7 – 4)x + (2 – 6)y + (–8 – 3)z 4x + 6y + 3z (Changing the sign)
– – –
= 3x – 4y – 11z 3x – 4y – 11z

2
2
2
Example 5: From the sum of 3y + y – 5 and –2y + 4y – 6, subtract 4y – 7y + 8.
2
2
Solution: The sum of 3y + y – 5 and –2y + 4y – 6 is: Try These
2
3y + y – 5
2
–2y + 4y – 6 1. What should be added to
2 2
2 2
6x y – 5xy to get 7x y + 6xy?
2
y + 5y – 11 2. If x = 3a + 2b and y = 3a – 2b,
2
2
The difference between y + 5y – 11 and 4y – 7y + 8 is: find (2x + 2y) – (3x + 3y) in terms
of a and b.
2
y + 5y – 11
2
4y – 7y + 8
– + – (Changing the sign)
2
–3y + 12y – 19
Example 6: If A = 2x – 5y, B = 6x + 3y and C = 2y – 3x, find 2A – 3B + 4C.
Solution: 2 A – 3B + 4C = 2(2x – 5y) –3(6x + 3y) + 4(2y – 3x)
= 4x – 10y – 18x – 9y + 8y – 12x
= (4 – 18 – 12)x + (–10 – 9 + 8)y
= –26x – 11y

EXERCISE 12.2

1. Add the following.
–1
2
3
3
3
2
3
(a) 3ab, 2ab, 2 ab (b) 4xy , – 6xy , –20xy , 5xy (c) 0.5x , 0.3x , –2.5x 2
2. Subtract the following.
4 6 1 2
2
2
2
(a) pq from pq (b) –3ab c from 5ab c (c) x y from 3x y
5 5 2
3. Add the following algebraic expressions.
(a) 4x + 3y + 8z, 6x – 2y + 7z, 8x + 7y + 3z (b) 3x + 7y – 9z – 15, 4x – 3y – 3z + 5
3
2
3
2
3
2
3
3
2
3
2
(c) 8x – 3x , –7x – 4x , 3x + 5x (d) 4x – 3x + 3x + 8, 6x – 7x + 4x, –8x + 7x 2
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