# From 7x^{2} – 4x subtract 5x^{2} + 2x

Arithmetic is the branch of mathematics in which we study numbers and operators, Geometry is the branch in which we study the shape and the dimensions, similarly, algebra is the branch of the mathematics in which we study to find the value of the unknown. Algebra consists of numerals, variables, and arithmetic operators. The terms having constant value are known as numerals and are represented by numbers, the terms that do not have constant value are known as the variables and are represented by the letters.

**Algebraic Expression**

An algebraic expression is the representation of a mathematical statement into mathematical terms with the help of numerals, variables, and operators. For example: ‘4 times a number is subtracted from 5’ can be written as ‘5-4x’.

Here we don’t know the value of unknown so we assume it as x. In the expression ‘5-4x’, negative separates the expression into two terms. So on the basis of the number of terms an algebraic expression is classified into the following categories.

**Monomial:**If the number of the terms in an expression is one then the expression is known as the monomial. Example: 5x, 3t, etc.**Binomial:**If the number of terms in an expression is two then the expression is known as binomial. Example: 5a+2b, 5e-6f, etc.**Trinomial:**If the number of expressions in an expression is three then the expression is known as the trinomial. Example: a+b+c, 5q-r+6s, etc.**Polynomial:**If the number of terms in an expression is one or more than one then the expression is known as the polynomial.

Like and unlike termsIf the variable part of an expression is the same then the terms are known as the like terms and if the variable part of the expression is not the same then the terms are known as the, unlike terms.

Example: 8y² – 6y³ + 3y – 6y² – 3y³ – 18

In the above expression, 8y² and 6y² have the same variable, 6y³ and 3y³ have the same variable part, so these terms are known as like terms.

### From 7x^{2} – 4x subtract 5x^{2} + 2x

**Solution:**

Step to solve the problem:

Step 1:Write the statement in mathematical expression with the help of operators.= (7x² – 4x) – (5x² + 2x)

Step 2:Open the bracket by distributive property of sign i.e. a – (b+c) = a – b – c= 7x² – 4x – 5x² – 2x

Step 3:Do the operation on the like terms according to the sign.= 2x² – 6x

Step 4:If there is a common factor in all the terms then take them out and write the expression in the simplest form.= 2×x×x – 2×3×x

= 2x × (x – 3)

So the translation of 5x² + 2x subtracted from 7x² – 4x into the mathematical expression is 2x(x – 3).

### Similar Questions

**Question 1: From 6y² – 2y subtract 3y² + y. Translate into an expression.**

**Solution:**

Write the statement in mathematical expression with the help of operators.

= (6y² – 2y) – (3y² + y)

Open the bracket by distributive property of sign i.e. a – (b+c) = a – b – c

= 6y² – 2y – 3y² – y

Do the operation on the like terms according to the sign.

= 3y² – 3y

If there is a common factor in all the terms then take them out and write the expression in the simplest form.

= 3×y×y – 3×y

= 3y (y – 1)

So the translation of 3y² + y subtracted from 6y² – 2y is 3y(y – 1).

**Question 2: From 9x² – x + 12 subtract 3x² + x + 12. Translate into an expression.**

**Solution:**

Write the statement in mathematical expression with the help of operators.

= (9x² – x + 12) – (3x² + x + 12)

Open the bracket by distributive property of sign i.e. a – (b+c) = a – b – c

= 9x² – x + 12 – 3x² – x – 12

Do the operation on the like terms according to the sign.

= 6x² – 2x

If there is a common factor in all the terms then take them out and write the expression in the simplest form.

= 2×3×x×x – 2×x

= 2x(3x – 1)

So the translation of 3x² + x + 12 subtracted from 9x² – x + 12 is 2x(3x – 1).