TMUA Algebraic Techniques & Manipulation — Questions and Answers

Question 1: Simplify: 2x + 3x - 5

6x
5x - 5 (Correct answer)
5x + 5
2x - 2

Correct answer: 5x - 5

To simplify the expression, combine the like terms. The terms 2x and 3x are like terms, so adding them together gives 5x. The constant term -5 remains unchanged, resulting in the simplified expression 5x - 5.

Question 2: Solve for x: 3x = 12

2
3
4 (Correct answer)
5

Correct answer: 4

To solve for x, you need to isolate x on one side of the equation. Divide both sides of the equation 3x = 12 by 3. This yields x = 12 / 3, which simplifies to x = 4.

Question 3: Factor: x² - 9

(x - 3)(x + 3) (Correct answer)
(x - 9)(x + 1)
(x - 1)(x + 9)
(x + 3)(x + 3)

Correct answer: (x - 3)(x + 3)

This expression is a difference of squares, which follows the algebraic identity a² - b² = (a - b)(a + b). Here, a = x and b = 3 (since 3² = 9). Therefore, x² - 9 factors into (x - 3)(x + 3).

Question 4: Expand: (x + 2)(x - 2)

x² + 4
x² - 4 (Correct answer)
x² + 2x - 2
x² - 2x + 2

Correct answer: x² - 4

This is an example of the difference of squares formula, (a + b)(a - b) = a² - b². Here, a = x and b = 2. So, expanding (x + 2)(x - 2) directly results in x² - 2². This simplifies to x² - 4.

Question 5: What is the solution to the equation x² = 16?

x = 4
x = -4
x = ±4 (Correct answer)
x = 8

Correct answer: x = ±4

To solve for x, take the square root of both sides of the equation. The square root of 16 is 4, but it's important to remember that both positive and negative values, when squared, will result in a positive number. Therefore, x can be either 4 or -4, denoted as x = ±4.

Question 6: Simplify: (2x)(3x)

5x
6x² (Correct answer)
5x²
6x

Correct answer: 6x²

To simplify this expression, multiply the coefficients (the numbers) and then multiply the variables. So, 2 * 3 = 6, and x * x = x². Combining these gives the simplified expression 6x².

Question 7: Solve: 2(x - 3) = 10

6
7
8 (Correct answer)
9

Correct answer: 8

First, distribute the 2 on the left side: 2x - 6 = 10. Next, add 6 to both sides of the equation: 2x = 16. Finally, divide both sides by 2 to solve for x: x = 8.

Question 8: If f(x) = x² + 2x, find f(2)

6
8 (Correct answer)
10
12

Correct answer: 8

To find f(2), substitute x = 2 into the function's equation. So, f(2) = (2)² + 2*(2). This calculates to 4 + 4, which equals 8.

Question 9: What is the value of x in the equation 5x - 10 = 0?

1
2 (Correct answer)
3
4

Correct answer: 2

To solve for x, first add 10 to both sides of the equation: 5x = 10. Then, divide both sides by 5 to isolate x: x = 10 / 5. This simplifies to x = 2.

TMUA Algebraic Techniques & Manipulation

Simplify: 2x + 3x - 5