Simplify the expression (11/10/22) × z

Algebra is the study and manipulation of mathematical symbols. The expressions of algebra are composed of known numbers and unknown values. These unknown quantities are determined by some basic algebraic operations. Some of the basic standard formulas are derived to carry out these calculations. 

Algebraic expressions

Algebraic expressions are the mathematical expressions that involve integer constants, variables, coefficient of variables, and power on the head of variables. These expressions are tied together with different algebraic operations.

Types of algebraic operations on the basis of the number of terms.

• Monomial expressions: Monomial expressions are an algebraic expression that only has one term. For example: 5x, 2y, +1 are some monomial expressions.
• Binomial expressions: Binomial expressions are algebraic expressions having two terms. For example: 2x + 3, x+ y, etc are some binomial expressions.
• Polynomial expressions: Polynomial expressions are algebraic expressions having multiple terms. For example: ab + bc + ca, x + xy + 1, etc are some polynomial expression.

Basic algebraic formula

The basic algebraic formulae are used in the calculations of maths. The formulas for determining unknown values or carrying out the algebraic operations are given below.

• 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 expression

Solution:

The following steps can be used to solve the problem,

• Simplifying the given algebraic expression

= 11/10/22 . z

• Dividing the numbers infraction

= 11/10 × 1/22 . z

• Multiplying the numbers into a single fraction

= 1/20 . z

• Multiplying z with 1.

= z/20

Hence, the solution for the given expression is z/20.

Sample Problems

Question 1: Simplify, 10 + 3(x – 5) – (2x – 9)

Solution:

= 10 + 3(x – 5) – (2x – 9)

= 10 + 3x – 15 – 2x + 9

= 3x – 2x – 15 + 9 + 10

= x + 4

Question 2: Simplify, 3 – 2(5 – x) – (3x + 7)

Solution:

= 3 – 2(5 – x) – (3x + 7)

= 3 – 10 + 2x – 3x – 7

= -x – 14

Question 3: Simplify, 6m² – 9m + 5m – 3m² + 10

Solution:

= 6m² – 9m + 5m – 3m² + 10

= 6m² – 3m² – 9m – 5m + 10

= 3m² – 4m + 10