Question

Factor 25x2 – 16.

A. (5x – 4)2
B. (5x + 1)(5x – 1)
C. (5x + 4)2
D. (5x + 4)(5x – 4)

Answer 1

The answer is D. (5x+4) (5x-4)

What I did was multiply. So the first step I did was take 5x and mutiplied it by 5x which gave me 25x2. Then after that I took 5x and muliplied it by -4 which gave me -20x.

The second step was taking 4 and multiplied it by 5x which would be +20x and then 4 x -4 would be -16 so when you write it down your problem is gonna be like this: 25x2 - 20x +20x -16

Last step! is to cross out both 20x's cause it's going to be 0 but the thing is you do not put the 0 in just leave it blank so your answer is 25x2 - 16. Hope this helps! :)

~Shadow

Answer 2

D. (5x + 4)(5x – 4)

Explanation:

This is the difference of two squares

`a^(2) - b^(2)  = (a-b)(a+b)\\`

Following from above,

25
`25x^(2) -16`

Taking the elements of the expression

`25x^(2) = 5^(2)x^(2)`

Using the law of indices,

`a^(2) b^(2) = (ab)^(2)`

`25x^(2) = (5x)^(2)`

`16 = 4^(2)`

Therefore,

`25x^(2) -16` =
`(5x)^(2)  - 4^(2)`

=
`(5x-4)(5x+4)`

Hence the correct answer is Option D.