## Math 7 Chapter 4 Lesson 1: The concept of algebraic expressions

## 1. Summary of theory

– Expressions that include addition, subtraction, multiplication, division, and exponential operations not only on numbers but also on letters are called algebraic expressions.

**Eg:** \(4x; 2(5+x); (x+y)^2; x^3;xy;\frac{150}{t-1};…\) are algebraic expressions.

In algebraic expressions, letters can represent arbitrary numbers. People call such words as variables (referred to as variables).

**Attention: **

– In algebraic expressions, because letters represent numbers, when performing operations on letters, we can apply the same properties and rules of operations as on numbers (commutative, associative, omitted) brackets, transition rules,…)

**Eg:** \( xy = yx, xxx = x^3, (x + y) + z = x + (y + z),\)

\(xy)z = x(yz), x(y + z) = xy + xz\)

– Expressions with variables in the form are quite complex, not considered in this chapter.

**Eg:** \(\frac{150}{t-1}; \frac{20}{y^2}\).

## 2. Illustrated exercise

**Question 1: **Write an algebraic expression that represents

a) Perimeter of a square whose side is a.

b) Perimeter of a rectangle whose length and width are x and y respectively.

c) Area of a parallelogram whose base is a and its height is h.

d) The distance traveled (s) by a motorcycle with a speed of 40 km/h in time t (h).

**Solution guide**

a) The algebraic expression for the square’s perimeter is 4a.

b) The algebraic expression for the perimeter of the rectangle is 2(x + y).

c) The algebraic expression for the area of a parallelogram is: ah

d) The algebraic expression for the distance traveled is: s = 40.t.

**Verse 2: **A businessman saves money in a bank is a (dong). The bank’s monthly interest rate is x%. Write an algebraic expression representing this businessman’s amount after one month, two months, one year (one year has 12 months).

**Solution guide**

After one month, with interest x%, this businessman gets a profit of ax% (VND)

Then, the businessman’s money after one month is a+ax%=a(1+x%) (VND)

In the second month, the businessman earns a profit of a(1+x%).x% (VND)

Then the businessman’s money after two months will be a(1+x%)+a(1+x%).x%=a(1+x%)(1+x%)=a(1+x %)^{2}

Keep doing this until a year, the businessman’s money after one year is a(1+x%)^{twelfth} (a year has 12 months).

## 3. Practice

### 3.1. Essay exercises

**Question 1: **Write an algebraic expression that represents:

a) Sum of two times x and three times y.

b) The difference of x and y.

c) The product of the sum of x and y with the difference of x and y.

**Verse 2:** Write an algebraic expression that represents:

a) Perimeter of a square whose side is a.

b) Perimeter of a rectangle whose length and width are x and y respectively.

c) The area of a parallelogram whose base is a and its height is h.

d) The distance traveled(s) by a motorbike with a speed of 40km/h in time t(h).

**Question 3: **The water in the kettle is at a temperature of t degrees. After heating for a while, the temperature of the water in the tank increased to y degrees compared to the original, suddenly the power was cut off, for a long time the temperature of the water in the tank dropped to x degrees compared to the original. Write an algebraic expression that represents the temperature when the water in the flask increases by y degrees from the beginning and decreases by x degrees from the beginning.

### 3.2. Multiple choice exercises

**Question 1: **Write an algebraic expression that expresses the following: Product of three numbers a, b and c

A. abc

B. ab+c

C. 3abc

D. a+bc

**Verse 2: **Write an algebraic expression that shows the following: Product of 3 times y with difference of squares of x and y

A. 3y(x-y)^{2}

B. (3y−x^{2})y^{2}

C. 3y(x^{2}-y^{2})

D. 3y.x^{2}.y^{2}

**Question 3: **Which of the following expressions represents the perimeter of an equilateral triangle with side length a?

A. 3a

B. 2a

Shift

D. a^{2}

**Question 4: **Make an algebraic expression representing the sum of 5 times x and 9 times y:

A. \((5+x)+(9+y)\)

B. \((5+x)-(9+y)\)

C. \(5x-9y\)

D. \(5x+9y\)

**Question 5: ** A businessman saves money in a bank is a (VND). The bank’s monthly interest rate is x%. Write an algebraic expression representing this businessman’s money after three months

A. a(1+x%) (VND)

B. a(1+x%)^{2} (copper)

C. a(1+x%)^{3} (copper)

D. a(1+x%)^{4} (copper)

## 4. Conclusion

Through this lesson, you should know the following:

- Master the concept of algebraic expressions.
- Do related exercises.

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