Page 92 - Start Up Mathematics_8 (Non CCE)

Subtraction of Algebraic Expressions

To subtract one algebraic expression from the other, first change the signs of all the terms of the expression
which have to be subtracted and then add the two expressions.

Subtraction can also be done by the column method.

6 4 3 5 a 3 5 1 3
Example 3: Subtract a - a + a + from - a + + a.
2
3
2
5 5 2 6 3 2 4 5
a 3 5 1 3 Ê 6 4 3 5ˆ
3
Solution: - a + + a - Á a - a + a + ˜
2
2
3 2 4 5 Ë 5 5 2 6¯
a 3 5 1 3 6 4 3 5
2
3
2
= - a + + a - a + a + a -
3 2 4 5 5 5 2 6
Ê a 3 4 ˆ Ê - 5 6 2 ˆ Ê 3 3 ˆ Ê 1 5ˆ
= Á + a 3 ˜ + Á a - a ˜ + Á a - a + Á - ˜ (Combining the like
2
˜
Ë 3 5 ¯ Ë 2 5 ¯ Ë 5 2 ¯ Ë 4 6¯ terms together)
Ê 5a + 12a ˆ Ê - 25a - 12a ˆ Ê 6a - 15aˆ Ê 310ˆ
-
3
2
3
2
= Á 15 ˜ Á 10 ˜ ¯ + Á 10 ˜ ¯ + Á 12 ¯ ˜
+
Ë Ë
Ë
Ë
¯ Ë
17 37 9a 7
2
3
= a - a - -
15 10 10 12
Ê 1 4 ˆ Ê 1 2 ˆ Ê 2 2 ˆ
2
2
Example 4: Simplify: Á Ë 3 x - 7 x + 11 - Á Ë 7 x - 32x+ ˜ - Á Ë 7 x - 3 x + 2 ˜ ¯
˜
¯
¯
ˆ
2
Solution: Ê 1 x - 4 x + 11 - Ê Á Ë 1 x - 32x+ 2 ˆ ˜ ¯ - Ê 2 x - 2 x + 2 ˆ
2
Á
˜
Á
˜
Ë
¯
Ë
¯
7
7
3
7
3
1 4 1 2 2
2
2
= x - x + 11 - x + 32x- 2 - x + x - 2
3 7 7 7 3
Ê 1 2 2 ˆ Ê 4 1 2 ˆ
2
= Á x - 2x + x ˜ +- x - x - x +( 11 32+ - ) (Combining the
2
Á
˜
Ë 3 3 ¯ Ë 7 7 7 ¯ like terms together)
2
Ê x - 6 x + 2 x ˆ Ê - 4 - - x
2
2
x x 2 ˆ
= Á 3 ˜ ¯ + Á Ë 7 ˜ ¯ + 12
Ë
-3x 2 7x
x
= - +12 =-x 2 -+12
3 7
2
2
2
2
Example 5: Subtract 2x + 9xy – 4x + 3 from 5xy – 6x + 7x – 9.
Solution: 5xy - 6x + 7x - Ô
2
2
9¸
˝ Writing like terms one beloww the other
2
2
9xy + 2x - 4x + 3Ô
˛
()- ()- () ()+ -
(In subtraction, thhe sign changes)
- 4xy 2 -8x 2 +11x -12
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