Question

Which products result in a difference of squares? Check all that apply. (5z + 3)(–5z – 3) (w – 2.5)(w + 2.5) (8g + 1)(8g + 1) (–4v – 9)(–4v + 9) (6y + 7)(7y – 6) (p – 5)(p – 5)

Answer 1

Answer:

(w - 2.5)(w + 2.5)

(-4v - 9)(-4v + 9)

Step-by-step explanation:

* Lets explain what is the a difference of two squares

- If we multiply two binomial and the answer just two terms with

 negative sign between them and the two terms are square numbers

 we called this answer a difference of two squares

- Examples

# (a + b)(a - b)

- Lets multiply them

∵ (a × a) + (a × -b) + (b × a) + (b × -b)

∴ a² - ab + ba - b²

- Add the like term

∵ ab = ba

∴ -ab + ba = 0

∴ (a + b)(a - b) = a² - b² ⇒ difference of two squares

- From above the difference of two squares appears when we

 multiply sum and difference of the same two terms

# (a + b) ⇒ is the sum of a and b

# (a - b) ⇒ is the difference of a and b

* Now lets solve the problem

- In (5z + 3)(-5z - 3)

∵ (5z + 3) ⇒ is the sum of 5z and 3

∵ (-5z - 3) ⇒ is the difference of -5z and 3

∵ 5z ≠ - 5z

∴ They are not the sum and difference of the same two terms

∴ The product result not in a difference of squares

- In (w - 2.5)(w + 2.5)

∵ (w - 2.5) is the difference between w and 2.5

∴ (w + 2.5) is the sum of w and 2.5

∴ They are the sum and difference of the same two terms

∴ The product result in a difference of squares

- In (8g + 1)(8g + 1)

∵ The two brackets are the sum of 8g and 1

∴ They are not the sum and difference of the same two terms

∴ The product result not in a difference of squares

- In (-4v - 9)(-4v + 9)

∵ (-4v - 9) is the difference between -4v and 9

∵ (-4v + 9) is the sum of -4v and 9

∴ They are the sum and difference of the same two terms

∴ The product result in a difference of squares

- In (6y + 7)(7y - 6)

∵ (6y + 7) is the sum of 6y and 7

∵ (7y - 6) is the difference between 7y and 6

∵ 6y ≠ 7y and 7 ≠ 6

∴ They are not the sum and difference of the same two terms

∴ The product result not in a difference of squares

- In (p - 5)(p - 5)

∵ The two brackets are the difference of p and 5

∴ They are not the sum and difference of the same two terms

∴ The product result not in a difference of squares

Answer 2

Answer: The correct options are B: (w – 2.5)(w + 2.5) and D: (–4v – 9)(–4v + 9).

i just did the assignment and got it right

hope this helps :3