A series of exercises on remarkable identities and literal calculus in the third grade (3ème).These exercises are intended for teachers and students of the third grade who wish to revise the chapter on remarkable identities and literal calculus online.
To continue the notions seen in fifth grade (simple distributivity) and in fourth grade (double distributivity),
you will find in this series of mathematical exercises on literal calculation, the following notions :
- definition of an algebraic or literal expression;
- reduce and expand a literal expression;
- factor a literal expression;
These corrected exercises of maths in third grade (3ème) have been written by a maths teacher
and can be viewed online or downloaded in PDF format.
Expand and reduce each expression.
Expand and reduce the following expression:
In each case, only one answer is correct.
Copy the correct answer.
a. If we expand and reduce the expression (x + 2)(3x-1),
we obtain :
b. The expanded form of is:
or or .
c. A factorized expression of is:
or or .
d. A factorized expression of is :
or or .
a. Give the result provided by the calculation program if we choose as
number of departures :
-2; 5 then 10.
b. Show that the result is always the square of a whole number.
The unit of length is the centimeter.
x denotes a number (x > 1).
a. For what value of x is the perimeter of the quadrilateral QUAD 32 cm ?
b. What is then the quadrilateral nature of QUAD?
AENT is a square with a perimeter of 56 cm.
PAE is an isosceles triangle at P.
a. Calculate AE.
b. For what length of [AP] is the perimeter of the pentagon PENTA equal to 60 cm? Justify.
Expand the following literal expressions:
x denotes a number greater than or equal to 2.
ABCD is a square and ABEF is a rectangle.
1. Express as a function of x;
a. the length AD ;
b. the area of the square ABCD ;
c. the area of rectangle ABEF ;
d. the area ‘ of the ECDF rectangle.
2. a. Express the areas and and their sum in expanded and reduced form.
b. Check that this sum is equal to .
Here are two calculation programs.
a. Apply each program to the numbers :
3; 10 and – 5 and then to another randomly chosen number
What do we see? Make a conjecture.
b. We note n the number chosen at the beginning.
Express the result obtained with each program as a function of n.
Prove the conjecture made in question a.
x is a positive number.
Here is a rectangle with sides of varying lengths.
a. Léa has built the program below with the Scratch software.
What do the variables l and L represent?
b. What is the role of Lea’s program?
c. Lea says:”.”
Is she right? Explain.
d. Carry out this program. Test it by giving x the value 3, then the value 10.
Associate each expression on the left with its factorized form on the right.
4) Calculate C for .
Develop using the indicated model.
Square of a sum | Square of a difference
We know that multiplying the sum of two numbers by their difference gives :
I=(x+8)(x-8) and J=(t-5)(t+5).
Factor each expression with a remarkable identity.
Recognize a difference of two squares in each expression, then factor.
Reduce each expression using a remarkable identity.
Expand and collapse each expression.
x is a relative number.
Using remarkable identities, copy and complete the table below.
Copy and complete using a remarkable identity.
- Recall the three remarkable identities.
- We want to develop :
- Which one will we use? Then specify the value of a and b.
- What is the development of ?
Complete and finish developments:
Same exercise as the previous one.
Expand then reduce :
State the factorized form of these expanded remarkable identities:
Factor the following expressions:
1) Expand then reduce .
2) We pose .
3) Without using the calculator and using question 1, find the value of D.
We give .
1) Expand and reduce E.
2) Factorize E.
3) Expand the expression obtained in question 2.
What is the result
We give .
1) Show that E can be written .
2) Calculate E for: ; .
3) Factor E. Expand the resulting expression.
What is the result?
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