Corrected algebraic calculus exercises

Exercise example N°1239 :

Expand the following expression `2*(8+x)`?

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This exercise allows to practice developing an algebraic expression by using different techniques of algebraic calculation.

Exercise example N°1240 :

Factor the following expression `12+4*x`.

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This exercise allows to practice factoring an algebraic expression by using different techniques of algebraic calculation.

Exercise example N°1325 :

Simplify the following expression `1+5*z+2*z^2+5+4*z+z^2+4+2*z+5*z^2`.

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This exercise allows you to practice the techniques of simplifying algebraic expressions that contain a single letter.

Exercise example N°1326 :

Expand the following expression `(-4*a-8*b)*(5*a+3*b)`.

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The objective of this algebraic calculus exercise is to expand an algebraic expression.

Exercise example N°1327 :

Compute the following expression `2+x+9+4*y` for x=4 ,y=6.

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The objective of this exercise is to calculate an algebraic expression by replacing letters with a given value.

Exercise example N°1328 :

Compare the following two expressions `90/10` ... `27/10`.

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The objective of this solved exercise is to compare two fractions using the correct operator.

Exercise example N°1330 :

I have a number, I add 27 to it, I subtract 22 from the result and I get 43, what is this number?

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The objective of this math exercise is to equate a simple problem to solve it.

Exercise example N°1336 :

Solve the following equation: 4*y-4=6.

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The purpose of this exercise is to solve a linear equation of the first degree with one unknown of the form ax+b=c.

Exercise example N°1337 :

Solve the following equation: 2*x+3=5.

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The purpose of this corrected exercise is to solve an equation with one unknown of the first degree of the form x+b=c.

Exercise example N°1338 :

Solve the following equation: 4*z+3=6*z+8.

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The purpose of this corrected exercise is to solve an equation with one unknown of the first degree of the form ax+b=cx+d.

Exercise example N°1339 :

My quadruple is equal to 32. Who am I?

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The purpose of this corrected math exercise is to solve an equation written in natural language.

Exercise example N°1340 :

In a class of 10 students 70 % got the average on the last test. What is the number of students who did not get the average?

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The purpose of this exercise is to solve a numerical problem by calculating the percentage of a whole number.

Exercise example N°1341 :

In a class of 10 students, 4 got the average in the last math test. What percentage of students got the average?

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The purpose of this math exercise is to calculate a percentage from two numbers.

Exercise example N°1342 :

In a class of 30 students there are 9 boys. What is the percentage of boys in this class?

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The purpose of this math exercise is to determine a percentage from two given integers.

Exercise example N°1412 :

Using the appropriate special expansion develop the following expression `(8*a+5*b)*(8*a-5*b)`.

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The purpose of this exercise is to develop an algebraic expression using the most suitable remarkable identity.

Exercise example N°1413 :

Using the appropriate remarkable identity calculate the following expression `999^2`.

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The purpose of this exercise is to calculate the square of a number using a remarkable identity.

Exercise example N°1430 :

Factor the following expression `x^2-20*x`.

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The purpose of this corrected algebraic calculus exercise is to factor an algebraic expression that involves squares.

Exercise example N°1431 :

Factor the following expression `9*x^2-49`.

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The purpose of this exercise is to factor an algebraic expression using a remarkable identity of the form a² - b².

Exercise example N°1631 :

1. Expand and reduce the following polynomial:`(-6+x^2)*(-5-4*x)`.
2. What is its degree ?

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The purpose of this exercise is to practice developing a polynomial and determining its degree.

Exercise example N°1632 :

1. Expand and reduce the following polynomial:`(7+x)^2-1-2*x+x^2+x^3`.
2. What is its degree ?

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The goal of this exercise is to practice developing a polynomial with remarkable identities and determining its degree.

Exercise example N°1633 :

P is the polynomial defined by P(x) =`-4+8*x+3*x^2-x^3`
1. Compute P(-2)
2. Find the polynomial Q such that for any real x, P(x)=(x+2)Q(x)

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The goal of this exercise of algebraic calculation is to factor a polynomial of degree 3 knowing one of its roots.

Exercise example N°1634 :

Compute the roots of P(x) =`-4+8*x+3*x^2-x^3`.

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The goal of this exercise of algebraic calculation is to determine the values for which a polynomial of degree 3 is equal to 0.