EQUIVALENT EXPRESSIONS WORKSHEET

Write the equivalent algebraic expressions for the following :

Question 1 :

7(x - 3) + 2(2x - 5) - 3(x - 5)

Question 2 :

4x - (2 + 4x) - 2(x - 1) - 8(x -3)

Question 3 :

(x + 3)² - (x - 3)²

Question 4 :

Question 5 :

Question 6 :

Question 7 :

Question 8 :

Question 9 :

Question 10 :

Question 11 :

Which of the following expressions is equivalent to 6x - 3 for all real values of x?

(A) 2(3x - 3)

(B) 3(2x - 3)

(C) 2(3x + 1) - 5

(D) 6(x - 3) 

(E) 6(x - 1) - 1

Question 12 :

If (x + 3)(x + a) = x² + bx + 6, find the value of 'a' and 'b'.

Question 13 :

You and four of your friends go to a movie and each buy popcorn.

a)  Use the Distributive Property to write an expression for the total cost to buy movie tickets and popcorn. Simplify the expression.

b) Choose a reasonable value for x. Evaluate the expression.

Question 14 :

The length of a rectangle is 16 inches, and its area is (32x + 48) square inches. Factor the expression for the area. Write an expression for the width.

Question 15 :

Evaluate the expression when x = 20 and y = 4.

a)  x ÷ 5

b)  y + x

c) 8y - x

Question 16 :

In a video game, you score p game points and b triple bonus points. An expression for your score is p + 3b. What is your score when you earn 245 game points and 20 triple bonus points?

1. Answer :

= 7(x - 3) + 2(2x - 5) - 3(x - 5)

Use Distributive Property.

= 7(x) + 7(-3) + 2(2x) + 2(-5) - 3(x) - 3(-5)

= 7x - 21 + 4x - 10 - 3x + 15

= 8x - 16

2. Answer :

= 4x - (2 + 4x) - 2(x - 1) - 8(x -3)

Use Distributive Property.

= 4x - 2 - 4x - 2(x) - 2(-1) - 8(x) - 8(-3)

= 4x - 2 - 4x - 2x + 2 - 8x + 24

= -10x + 24

3. Answer :

= (x + 3)² - (x - 3)²

= (x + 3)(x + 3) - (x - 3)(x - 3)

= (x² + 3x + 3x + 9) - (x² - 3x - 3x + 9)

= (x² + 6x + 9) - (x² - 6x + 9)

= x² + 6x + 9 - x² + 6x - 9

= 12x

4. Answer :

5. Answer :

6. Answer :

7. Answer :

8. Answer :

9. Answer :

10. Answer :

11. Answer :

Given expression : 6x - 3.

Options :

(A) 2(3x - 3)

(B) 3(2x - 3)

(C) 2(3x + 1) - 5

(D) 6(x - 3) 

(E) 6(x - 1) - 1

In the given expression, the coefficient of x is 6 and constant is -3.

In all the above options, the coefficient of x is 6. We have to find the option in which the constant is -3.

When you simplify the expression in option (C), the constant is -3.

Option (C) :

2(3x + 1) - 5 = 2(3x) + 2(1) - 5

= 6x + 2 - 5

= 6x - 3

So, the correct choice is option (C).

12. Answer :

(x + 3)(x + a) = x² + bx + 6

x² + ax + 3x + 3a = x² + bx + 6

x² + (a + 3)x + 3a = x² + bx + 6

Since the above two expressions are equal, coefficients of like terms also must be equal.

Equate the coefficients of x and constants.

Substitute a = 3 in (1).

b = 3 + 3

b = 6

Therefore,

a = 3 and b = 6

13. Answer :

a)  Number of adult ticket bought = 1

Number of student tickets = 4

Required cost = 10 + 4(8 + x)

= 10 + 32 + 4x

= 42 + 4x

b) When x = 2

= 42 + 4(2)

= 42 + 8

= 50

14. Answer :

Length = 16 inches

Area of rectangle = (32x + 48) square inches

48 = 3 ⋅ 16

32 = 2 ⋅ 16

Factoring 16, we get

= 16(2x + 3)

Width of the rectangle is 2x + 3.

15. Answer :

Evaluate the expression when x = 20 and y = 4.

16. Answer :

Game points p = 245

triple bonus point b = 20

p + 3b = 245 + 3(20)

= 245 + 60

= 305

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