What is the result of dividing 8 by 4?

Correct Answer: A

Rationale: Rationale: In this question, the correct answer is A) 2. When dividing 8 by 4, you are essentially looking for how many times 4 can fit into 8. By dividing 8 by 4, you get 2, because 4 goes into 8 two times evenly. Option B) 4 is incorrect because dividing 8 by 4 does not result in 4, but rather 2. Option C) 6 is incorrect as well, as it is not a valid result of dividing 8 by 4. Option D) 8 is also incorrect because when dividing a number by itself, the result is always 1, not 8. Educationally, understanding basic arithmetic operations like division is crucial for solving math problems accurately. Dividing numbers helps in understanding the concept of sharing or distributing quantities equally. It is essential for building a strong foundation in mathematics, which is necessary for various real-life applications and higher-level math concepts. Therefore, mastering these fundamental operations is key to success in mathematics.

Correct Answer: C

Rationale: When you see something like (a + b)², it means you're multiplying (a + b) by itself: (a + b)² = (a + b) (a + b) To expand this, we use the distributive property (which says you multiply each term in the first bracket by each term in the second bracket): Multiply the first term in the first bracket (a) by both terms in the second bracket: a a = a² a b = ab Multiply the second term in the first bracket (b) by both terms in the second bracket: b a = ab b b = b² Now, add up all the results from the multiplication: a² + ab + ab + b² Since ab + ab is the same as 2ab, we can simplify it to: a² + 2ab + b² So, (a + b)² = a² + 2ab + b². This is known as a basic polynomial identity, and it shows that when you square a binomial (a two-term expression like a + b), you get three terms: the square of the first term (a²), twice the product of the two terms (2ab), and the square of the second term (b²). Therefore, the correct answer is C (a² + 2ab + b²)

Correct Answer: D

Rationale: When simplifying the expression 3x - 5x + 2, start by combining like terms. -5x is subtracted from 3x to give -2x. Adding 2 at the end gives the simplified expression -2x. Therefore, the correct answer is -2x. Choice A, -2x + 2, incorrectly adds 2 at the end. Choice B, -8x, incorrectly combines the coefficients of x without considering the constant term. Choice C, 2x + 2, incorrectly adds the coefficients of x without simplifying.

Correct Answer: A

Rationale: The expression x^2 - y^2 is a difference of squares, which follows the identity: x^2 - y^2 = (x + y)(x - y). Therefore, the given expression becomes: (x^2 - y^2) / (x - y) = (x + y)(x - y) / (x - y). Since (x - y) appears in both the numerator and the denominator, they cancel each other out, leaving x + y. Thus, the simplified form of (x^2 - y^2) / (x - y) is x + y. Therefore, the correct answer is A (x + y). Option B (x - y) is incorrect as it does not result from simplifying the given expression. Option C (1) is incorrect as it does not account for the variables x and y present in the expression. Option D ((x + y)/(x - y)) is incorrect as it presents the simplified form in a different format than the correct answer.

Correct Answer: A

Rationale: To determine how many times larger the first cell is compared to the second cell, divide the diameter of the first cell by the diameter of the second cell: 0.1 / 0.05 = 2. Therefore, the first cell is 2 times larger than the second cell. Choice B, C, and D are incorrect because they do not provide the accurate calculation for the size difference between the two cells.