Subtract and Simplify (0.04x3-0.03x2+0.02x) – (0.03x3+0.08x2-6)

Mathematics is basically divided into different branches, out of which one branch is algebra. In algebra, people deal with numerals and variables, known value is termed as numerals and unknown value is termed as a variable. A variable can take any value. Arithmetic operations like addition, subtraction, multiplication, and division are also applied in algebra to find out the value of unknowns. 

Algebraic Expressions

An algebraic expression is the combination of numerals and variables in systematic order. Numerals and variables are related by four fundamental mathematical operators, addition, subtraction, multiplication, or division. Example: By using two numerals (5 and 6), and one variable x, one can form an algebraic expression 6x + 5. In this expression, there are two terms. So on the basis of the number of terms algebraic expression is categorized into the following types,

• Monomial: When an algebraic expression has only one term then that is known as a monomial. Example: 5t, 8y, etc
•  Binomial: When the number of terms in an algebraic expression is two then that expression is known as binomial. Example: 5t – 8k, 8t + 6, etc
• Trinomial: An algebraic expression having three-term is called a trinomial. Example: 6x – 3y – 5z, 9t – 6u + 7w, etc
• Polynomial: An algebraic expression having one or more than one term is known as a polynomial.

To perform the fundamental arithmetic operation in algebraic expression, find out the like and unlike terms. 

Like and Unlike Terms: The term having same variables are known as like terms and the terms which does not have same variable is known as unlike terms.

Example: In the algebraic expression, 5x +6y -7x² -4x +9, the terms which have same variables are 5x and 4x, so these two terms is called as like terms. 

Subtract and simplify: (0.04x³ – 0.03x² + 0.02x) – (0.03x³ + 0.08x² – 6)

Solution:

Steps to solve the problem

Step 1: Find out the like terms of the given algebraic expression.

Step 2: Apply the arithmetic operation on the numeral part of like terms.

Step 3: No operation is applied on unlike terms.

Step 4: By solving the like term, reduce the expression in the lowest term.

In the given algebraic expression, like terms are 0.04x³ and 0.03x³, 0.03x² and 0.08x².

The given expression can be written as,

= 0.04x³ – 0.03x² + 0.02x – 0.03x³ – 0.08x² + 6

= 0.04x³ – 0.03x³ – 0.03x² – 0.08x² + 0.02x + 6

On solving like terms,

= 0.01x³ – 0.11x² + 0.02x + 6

On simplifying the expression  (0.04x³ – 0.03x² + 0.02x) – ( 0.03x³ + 0.08x² – 6), we got 0.01x³ – 0.11x² + 0.02x + 6.

Similar Questions

Question 1: Subtract and simplify: (5x³ – 12x² – 6x + 12) – (12x² +6x – 10)

Solution:

In the given expression like terms are 12x² and 12x², 6x and 6x, 12 and 10.

The given expression can be written as 

= 5x³ – 12x² – 6x + 12 – 12x² – 6x +10

= 5x³ – 12x² – 12x² – 6x – 6x +12 +10

On solving the like terms,

= 5x³ – 24x² – 12x + 22

So, on simplifying the expression  (5x³ – 12x² – 6x + 12) – (12x² + 6x – 10), 

= 5x³ – 24x² – 12x + 22.

Question 2: Subtract and simplify: (0.5y³ – 0.03x² – 0.3z + 12) – (0.4y³ – 0.36x² + 0.2z – 11)

Solution:

In the given expression, like terms are 0.5y³ and 0.4y³, 0.03x² and 0.36x², and 0.3z and 0.2z, 12 and 11

The given expression can be written as,

= 0.5y³ – 0.03x² – 0.3z +12 – 0.4y³ + 0.36x² – 0.2z +11

= 0.5y³ – 0.4y³ – 0.03x² + 0.36x² – 0.3z – 0.2z + 12 + 11

On solving the like terms,

= 0.1y³ + 0.06x² – 0.5z + 23

So, on solving the expression (0.5y³ – 0.03x² – 0.3z + 12) – (0.4y³ – 0.36x² + 0.2z -11),

= 0.1y³ + 0.06x² – 0.5z + 23