Calculus: 3rd grade math course to download in PDF.

The course on literal calculus and the three remarkable identities with the definition of the development of a literal expression and factoring is very important for the student’s progress in math. The student will need to know how to expand and factor a literal expression and also, substitute a value.

In addition, they must be able to use remarkable identities well in order to develop algebraic computation skills. It is a chapter to understand in order to avoid complications during the control.

We will end this lesson on literal calculation with concrete examples from everyday life or from geometry in the third grade.

I. Literal Expression and Vocabulary:


A literal expression is an expression containing letters.

Example: 2x^2+5x+7


numerical calculation is a special case of literal calculation. Therefore, the literal calculus is a very powerful tool allowing us to deal with generalizations of situations.


Developing a literal expression means writing it as a sum of terms.

Property of simple distributivity:

Let k, a and b be three relative numbers.k(a+b)=ka+kb\\k(a-b)=ka-kb

Double distributivity property:

Let a, b, c and d be four relative numbers.(a+b)(c+d)=ac+ad+bc+bd


We have seen in the previous levels, two properties that allow to develop a literal expression: the simple and double distributivity.




Reducing a literal expression means grouping all terms of the same kind.




Definition of factoring:

To factor a literal expression is to write it as a product of factors.


Factoring is the reverse “process” of development.


A=7x-21=7x-7\times  ,3=7(x-3)


II. Remarkable identities

1.square of a sum


Let a and b be two relative numbers.(a+b)^2=a^2+2ab+b^2



2.square of a difference


let a and b be two relative numbers.(a-b)^2=a^2-2ab+b^2



3.product of a sum and a difference of two numbers with the literal calculation


Let a and b be two relative numbers.(a-b)(a+b)=a^2+ab-ab-b^2=a^2-b^2


A=(x+1)^2=x^2+2\times  \,x\times  \,1=x^2+2x+1\\B=(x-3)^2=x^2-2\times  \,x\times  \,3+3^2=x^2-6x+9\\C=(x-5)(x+5)=x^2-5^2=x^2-25\\D=99\times  \,101=(100-1)(100+1)=100^2-1^2=10000-1=9999\\E=(2x-7)^2=(2x)^2-2\times  \,2x\times  \,7+7^2=4x^2-28x+49

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