Question

Which equation is true?

9x2 – 25 = (3x – 5)(3x – 5)

9x2 – 25 = (3x – 5)(3x + 5)

9x2 – 25 = –(3x + 5)(3x + 5)

9x2 – 25 = –(3x + 5)(3x – 5)

Answer 1

The correct answer option is 9x2 – 25 = (3x – 5)(3x + 5).

Explanation:

To find out which of the equations is true, solve the right side of all the equations to check if they match the left side of the equation (which is same for every option).

1. (3x – 5)(3x – 5) = 3x^2 - 15x - 15x -10 = 3x^2 - 30x - 10 ---> False

2. (3x – 5)(3x + 5) = 3x^2 + 15x - 15x - 25 = 3x^2 - 25 ---> True

For equations 3 and 4, we do not even need to check because the terms are multiplied with a '-' sign making it negative.

Answer 2

B

Explanation:

Start by reasoning out what you need. Then calculate. You could just begin by removing the brackets on the right for each possible answer, but you are doing a little more work than you have to.

If the signs are the same inside the brackets, you will get a middle term and that is not the answer. For example

A

Remove the brackets on the right. (3x - 5)(3x - 5) = 9x^2 - 15x - 15x + 25 leaves you with 9x^2 - 30x + 25 which has a middle term and is not the answer.

C

Same thing as A

D is wrong because the - outside the brackets affects everything.

The answer must be B