Expansion of the square of trinomial

How to expand the square of a trinomial?

The square of the sum of three or more terms can be determined by the formula of the determination of the square of sum of two terms.

Now we will learn to expand the square of a trinomial (a + b + c).

Let (b + c) = x      

Then (a + b + c)² = (a + x)² = a² + 2ax + x²

                         = a² + 2a (b + c) + (b + c)² 

                         = a² + 2ab + 2ac + (b² + c² + 2bc) 

                         = a² + b² + c² + 2ab + 2bc + 2ca

Therefore, (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca


● (a + b - c)² = [a + b + (-c)]² 

                   = a² + b² + (-c)² + 2ab + 2 (b) (-c) + 2 (-c) (a) 

                   = a² + b² + c² + 2ab – 2bc - 2ca

Therefore, (a + b - c)² = a² + b² + c² + 2ab – 2bc - 2ca


● (a - b + c)² = [a + (- b) + c]²

                   = a² + (-b²) + c² + 2 (a) (-b) + 2 (-b) (-c) + 2 (c) (a) 

                   = a² + b² + c² – 2ab – 2bc + 2ca

Therefore, (a - b + c)² = a² + b² + c² – 2ab – 2bc + 2ca


● (a - b - c)² = [a + (-b) + (-c)]²

                   = a² + (-b²) + (-c²) + 2 (a) (-b) + 2 (-b) (-c) + 2 (-c) (a) 

                   = a² + b² + c² – 2ab + 2bc – 2ca

Therefore, (a - b - c)² = a² + b² + c² – 2ab + 2bc – 2ca



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Mathematical concept

What is a mathematical concept?

A:

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A mathematical concept is a general idea behind an equation, problem or formula in math. In contrast to a math fact, which must be committed to memory, a math concept explains why math works in a certain way.

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    A student who understands mathematical concepts advances to a higher level of learning involving abstract thinking. Understanding math concepts often negates the need to memorize answers to problems. Mathematicians use abstract thinking to formulate new theories, which they test by mathematical proof. Mathematical practices such as counting and measurement developed from initial abstraction and logical thinking. Math arises from thinking abstractly about many kinds of practical problems in disciplines such as architecture, astronomy and business.
    
    

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Mathematical formulas

Average formula: 

Let a₁,a₂,a₃,......,a_n be a set of numbers, average = (a₁ + a₂ + a₃,+......+ a_n)/n

Fractions formulas: 

Converting an improper fraction to a mixed number:

Formula for a proportion: 

In a proportion, the product of the extremes (ad) equal the product of the means(bc), 

Thus, ad = bc

Percent: 

Percent to fraction: x% = x/100

Percentage formula: Rate/100 = Percentage/base

Rate: The percent. 
Base: The amount you are taking the percent of.
Percentage: The answer obtained by multiplying the base by the rate

Consumer math formulas: 

Discount = list price × discount rate

Sale price = list price − discount

Discount rate = discount ÷ list price

Sales tax = price of item × tax rate

Interest = principal × rate of interest × time

Tips = cost of meals × tip rate

Commission = cost of service × commission rate