Contents
Step-wise procedure for subtraction of algebraic expressions by horizontal method:
Step 1) Write the expressions in one row with the expression to be subtracted in a bracket with assigning negative sign to it.
Step 2) Add the additive inverse of the second expression to the first expression.
Step 3) Group the like terms and add or subtract
Step 4) Write in standard form.
Example 1:
Subtract 3x + 4y – 2z from 3z + 6x – 2y.
Solution:
S.No |
Steps |
Process |
1 |
Write the expressions in one row with the expression to be subtracted in a bracket with assigning negative sign to it. |
3z + 6x – 2y – (3x + 4y – 2z) |
2 |
Add the additive inverse of the second expression to the first expression. |
3z + 6x – 2y – 3x – 4y + 2z |
3 |
Group the like terms and add or subtract |
(3z + 2z) + (6x – 3x) + (-2y – 4y) = 5z + 3x – 6y |
4 |
Write the resultant expression in standard form. |
3x – 6y + 5z |
Example 2:
Subtract \(a^2\) – 3ab from 2\(a^2\) – 7ab.
Solution:
S.No |
Steps |
Process |
1 |
Write the expressions in one row with the expression to be subtracted in a bracket with assigning negative sign to it. |
2\(a^2\) – 7ab – (\(a^2\) – 3ab) |
2 |
Add the additive inverse of the second expression to the first expression. |
2\(a^2\) – 7ab – \(a^2\) + 3ab |
3 |
Group the like terms and add or subtract |
(2\(a^2\) – \(a^2\)) – 7ab + 3ab |
4 |
Write the resultant expression in standard form. |
\(a^2\) – 4ab |
Example 3:
Subtract \(x^2\) – 3xy + 7\(y^2\) – 2 from 6xy – 4\(x^2\) – \(y^2\) + 5.
Solution:
S.No |
Steps |
Process |
1 |
Write the expressions in one row with the expression to be subtracted in a bracket with assigning negative sign to it. |
6xy – 4\(x^2\) – \(y^2\) + 5 – (\(x^2\) – 3xy + 7\(y^2\) – 2) |
2 |
Add the additive inverse of the second expression to the first expression. |
6xy – 4\(x^2\) – \(y^2\) + 5 – \(x^2\) + 3xy – 7\(y^2\) + 2 |
3 |
Group the like terms and add or subtract |
(6xy + 3xy) – 4\(x^2\) – \(x^2\) – \(y^2\) – 7\(y^2\) + 5 + 2 |
4 |
Write the resultant expression in standard form. |
9xy – 5\(x^2\) – 8\(y^2\) + 7 |