# Simplify 7x^{2} + 4.5y – 3y + x^{2} – 5x

There are different branches in mathematics, out of which one branch is algebra. In algebra, we deal with numerals and variables. The term which has a constant value is known as the numerals and the terms that do not have a constant value are known as variables. We generally represent numerals by numbers and variables by letters of the alphabet. The main use of algebra is to find the unknowns by assuming them as a letter or symbols.

**Algebraic Expression**

An algebraic expression is the combination of numerals, variables, and arithmetic operators. All these together are arranged in the systemic form to form a mathematical expression of the given statement. For example, The statement ‘ Six times a number is taken away from 15’ can be written as ‘ 15 – 6x ‘. In the expression 15 – 6x, minus sign separate the expression into two terms. So on the basis of the number of terms, the algebraic expression can be divided into the following types.

**Monomial:**If the number of terms in an expression is one then the algebraic expression is known as the monomial. Example: 5x, 8y, etc**Binomial:**If the number of terms in an algebraic expression is two then it is called binomial expression. Example: 8t-9r, 9a+2b, etc.**Trinomial:**If the number of terms in an algebraic expression is two then it is known as trinomial expression. Example: 5x+9y+3z, 8a+3b-3c, etc.**Polynomial:**If the number of terms in an expression is one or more than one then it is known as the polynomial.

Like and unlike terms:In an algebraic expression addition and subtraction is done only for like terms. In the expression, if the variable part of two or more different terms is the same then it is called like terms, and if the variable part is not the same then it is called, unlike terms.

Example: In the expression, 9x² + 25x -3x² -6y +3x + 7, 9x² and 3x² have the same variable, and 25x and 3x have the same variable and we name them like terms.

### Simplify 7x^{2} + 4.5y – 3y + x^{2 }– 5x

**Solution:**

Step to solve the problem:

Step 1:Find out the like terms in the given algebraic expression.= 7x² + 4.5y -3y +x² -5x

In the above expression, 7x² and x² have the same variable, 4.5y and 3y have the same variable.

= 7x² + x² +4.5y -3y -5x

Step 2:Do the calculation on like terms according to the arithmetic operators.= 8x² +1.5y -5x

So the simplified form of 7x

^{2}+ 4.5y – 3y + x^{2}– 5x is 8x² +1.5y -5x.

### Similar Questions

**Question 1: Simplify 9x² + 25x -3x² -6y +3x + 7**

**Solution:**

In the given algebraic , find out the like terms.

= 9x² + 25x -3x² -6y +3x + 7

9x² and 3x² have same variable, and 25x and 3x have same variable.

= 9x² -3x² +25x +3x -6y +7

Do the calculation on like terms according to the arithmetic operators.

= 6x² +28x – 6y +7

Further this expression can not be solved because all the terms in the expression is unlike terms.

So the simplification of 9x² + 25x -3x² -6y +3x + 7 is 6x² +28x – 6y +7.

**Question 2: Simplify: 5x³ +3x² -6x + 9x² -5x³ +7**

**Solution: **

In the given algebraic , find out the like terms.

= 5x³ +3x² -6x + 9x² -5x³ +7

5x³ and 5x³ are like terms, 3x² and 9x² are like terms because they have same variables.

= 5x³ -5x³ +3x² +9x² -6x +7

Do the calculation on like terms according to the arithmetic operators.

= 0 + 12x² -6x +7

=12x² -6x +7

So the simplification of 5x³ +3x² -6x + 9x² -5x³ +7 is 12x² -6x +7.