ADD SUBTRACT AND MULTIPLY LINEAR EXPRESSIONS
About "Add subtract and multiply linear expressions"
Add subtract and multiply linear expressions :
Whenever we want add or subtract linear expressions, we must know about combining like terms.
Like terms or Similar terms:
Like terms are the terms which have the same variables with same exponent for each variable.
Examples : 7x, 3x, - 4x
7x and -5xy are not like terms. Because in the first term we have the variable x only. But in the second term, we have x and y.So we cannot combine them.
To add or subtract linear expression, we have two methods
(i) Horizontal method
(ii) Vertical method
Horizontal method :
In this method, we arrange all the terms in a horizontal line and then add or subtract by combining the like terms.
Vertical method :
In this method, we should write the like terms vertically and then add or subtract.
Add subtract and multiply linear expressions - Examples
Let us look into some example problems to understand how to add subtract and multiply linear expressions.
Example 1 :
Add 6a + 3 and 4a - 2.
Solution :
Adding linear expressions in horizontal method :
= (6a + 3) + (4a - 2)
= 6a + 4a + 3 - 2
= 10a + 1
Adding linear expressions in vertical method :
Example 2 :
Add 5y + 8 + 3z and 4y - 5
Solution :
Adding linear expressions in horizontal method :
= (5y + 8 + 3z) + (4y - 5)
= 5y + 4y + 8 - 5 + 3z
= 9y + 3z + 3
Adding linear expressions in vertical method :
Example 3 :
Add 10x²- 5xy + 2y², -4x²+ 4xy + 5y², 3x²- 2xy - 6y²
Solution :
Adding linear expressions in horizontal method :
= (10x²- 5xy + 2y²) + (-4x²+ 4xy + 5y²) + (3x²- 2xy - 6y²)
= 10x² - 4x² + 3x² - 5xy + 4xy - 2xy + 2y²+ 5y² - 6y²
= 13x² - 4x² - 7xy + 4xy + 7y² - 6y²
= 9x² - 3xy + y²
Adding linear expressions in vertical method :
Example 4 :
Subtract 6a - 3b from - 8a + 9b.
Solution :
Subtracting linear expressions in horizontal method:
= (- 8a + 9b) - (6a - 3b)
Distribute the negative sign inside the parentheses
= - 8a + 9b - 6a + 3b
= -8a - 6a + 9b + 3b
= -14a + 12b
Subtracting linear expressions in vertical method :
Example 5 :
Subtract a² + b² - 3ab from a² + b² - 3ab
Solution :
Subtracting linear expressions in horizontal method:
= (a² - b² - 3ab) - (a²+ b² - 3ab)
= a² - b² - 3ab - a² - b² + 3ab
= a² - a² - b² - b² - 3ab + 3ab
= - b² - b²
= - 2b²
Subtracting linear expressions in vertical method :
Example 6 :
Multiply (3a - 2b) (2p + 3q)
Solution :
By using distributive property we can multiply two polynomials.
= (3a - 2b) (2p + 3q)
= 3a(2p + 3q) - 2b(2p + 3q)
= 6ap + 9aq - 4pb - 6qb
Since there is not like terms, we cannot combine any more.
Hence the answer is 6ap + 9aq - 4pb - 6qb.
Example 7 :
Multiply (3x - 7) (7x - 3)
Solution :
By using distributive property we can multiply two polynomials.
= (3x - 7) (7x - 3)
= 3x(7x - 3) - 7(7x - 3)
= 21x² - 9x - 49x + 21
= 21x² - 58x + 21
Hence the answer is 21x² - 58x + 21.
After having gone through the stuff given above, we hope that the students would have understood "Add subtract and multiply linear expressions".
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