Mathematics is categorized into different parts, out of which one part is Algebra. In algebra, we use numerals and variables. The term having a constant value is called numerals and the terms that do not have any constant value are termed as the variables. Numerals and variables are connected through arithmetic operators addition, subtraction, multiplication, and division. For the calculation of unknowns, we apply the arithmetic operation accordingly and get the answer.
Algebraic Expression
An algebraic expression is the combination of numerals and variables with the help of basic arithmetic operators like addition, subtraction, multiplication, or division. An algebraic expression is a mathematical form of writing a mathematical statement. It consists of numerals and variables along with arithmetic operators. The term which has constant value is termed as the numerals and the term which does not have constant value s termed as the variables.
For example,
‘A number is increased by 7’ can be written as the algebraic term ‘x + 7’
Here x is unknown, it can take any value and 7 is a fixed value. It is separated by + sign into two terms. On the basis of the number of terms, an algebraic expression can be divided into the following categories.
- Monomial: If the number of terms in algebraic expression is one then it is termed as a monomial. Example: 9x, 6a, etc
- Binomial: If the number of terms in algebraic expression is two then the algebraic expression is termed binomial expression. Example: 8x+3y, 9y+6z, etc.
- Trinomial: If the number of terms in an algebraic expression is three then the algebraic expression is termed trinomial. Example: 6a+3b+9c, 6x+2y+3, etc.
- Polynomial: If the number of terms in an algebraic expression is one or more than one the algebraic expression is termed as the polynomial.
Like and Unlike terms:
In an algebraic expression, if the variable part is the same then we call them like terms and if the variable part is not the same then we call it unlike terms. Addition and subtraction are done on the basis of like and unlike terms.
For example: In the algebraic expression ‘8x +5y + 6z + 8 + 7x +2a’, 8x and 7x is like term because they have same variable i.e. x.
Subtract (2x2–5x+7) from (3x2+4x–6).
Solution:
Step to solve the problem:
Step 1: Write the given statement in the algebraic expression.
= (3x² +4x -6) – (2x² -5x +7)
Step 2: Open the bracket by using the distributive property of subtraction i.e. {(a+b)-(c-d) = a + b -c +d}
Multiplication of (-)ve with (-)ve, (+)ve with (+)ve is (+)ve, and multiplication of (-)ve with (+)ve is (-)ve.
= 3x² +4x -6 – 2x² +5x -7
Step 3: Find out the like terms and apply the arithmetic operation.
= 3x² -2x² +4x +5x -6 -7
= x² + 9x -13
So the subtraction of (2x²–5x+7) from (3x²+4x–6) is x² + 9x -13.
Similar Questions
Question 1: Subtract (9x² -6x +8) from (15² -3x +2).
Solution:
Write the given statement in the algebraic expression.
= (15x² – 3x + 2) – (9x² -6x +8)
Open the bracket and simply the terms by using the distributive property of the negative sign.
= 15x² – 3x + 2 – 9x² + 6x – 8
Find out the like terms and apply mathematics operation.
= 15x² – 9x² -3x +6x +2 -8
= 6x² +3x -6
So, the subtraction of (9x² -6x +8) from (15² -3x +2) is 6x² +3x -6.
Question 2: Subtract (8x³ – 6x² + 13x -6) from (x³ -9).
Solution:
Write the given statement in the algebraic expression.
= (x³ -9) – (8x³ – 6x² + 13x -6)
Open the bracket and simply the terms by using the distributive property of the negative sign.
= x³ – 9 – 8x³ +6x² -13x +6
Find out the like terms and apply mathematics operation.
= x³ – 8x³ +6x² -13x -9 +6
= -7x³ +6x² -13x -3
So, the subtraction of (8x³ – 6x² + 13x -6) from (x³ -9) is -7x³ +6x² -13x -3.