Simplify 7x – 4x – x¹²

Algebra is a vital branch of mathematics in elementary education. According to the definition of algebra, it is a study of integers, mathematical symbols, and their analysis. Algebra includes components like variable, constant, integers, and mathematical operation. It is an analysis method for the derivation of unknown quantities. Many standard algebraic formulas are stated there for the purpose of determining unknown quantities.

Algebraic expressions

Algebraic expressions are the equations of algebra composed of known and unknown quantities. It consists of variables, constants, coefficient of the variable along with algebraic operation. They are the kind of mathematical expression that have components as integers, constants, variables, coefficient of variable and exponential power. The combined form of these components is known as terms. In every expression, these terms are bounded together with various mathematical operations like addition, subtraction, multiplication, or division.

On the basis of number terms involved in the expression they are divided into three categories,

• Monomial expression: These expressions consist of a single term. For example: 3xy, 3x,etc
• Binomial expression: These expressions consist of two terms. For example: 3x + 2, 2x + 5y,etc.
• Polynomial expression: These expressions consist of more than two terms. For example: xy + yz + zx, 3x + xy + 1,etc.

Basic formulas of algebra 

• a² – b² = (a – b)(a + b)
• (a + b)² = a² + 2ab + b²
• (a – b)² = a² – 2ab + b²
• a² + b² = (a – b)² +2ab.
• (a + b + c)² = a² + b² + c² + 2ab + 2ac + 2bc.
• (a – b – c)² = a² + b² + c² – 2ab – 2ac + 2bc.
• a³ – b³ = (a – b) (a² + ab + b²)
• a³ + b³ = (a + b) (a² – ab + b²)

Simplify the equation: 7x – 4x – x¹²

Solution:

Given algebraic expression

= 7x – 4x – x¹²

Step 1: Combining like terms

= 7x – 4x – x¹²

= 3x – x¹²

Step 2: Rearranging terms in descending order of exponent power

= 3x – x¹²

= -x¹² + 3x

Hence, the solution of the given equation is -x¹² + 3x.

Sample problems

Question 1: Simplify the equation: 2(x + 5) – 7 = 3(x – 2)

Solution:

2(x + 5) – 7 = 3(x – 2)

= 2x + 10 – 7 = 3x – 6

= -x + 3 = -6

x = 9

Question 2: Solve the equation: 5x² + 7x – 9 = 4x² + x – 18

Solution:

5x² + 7x – 9 = 4x² + x – 18

= 5x² + 7x – 9 – 4x² – x + 18 = 0

x² + 6x + 9 = 0

Question 3: If x = -2, what is the value of 3x + 5.

Solution:

According to the question,

x = -2

= 3x + 5

= 3(-2) + 5

= -6 + 5

= -1