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Factor 25x2 – 16.

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

Respuesta :

ShadowWolf18
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:

D. (5x + 4)(5x – 4)

Step-by-step explanation:

This is the difference of two squares

[tex]a^{2} - b^{2}  = (a-b)(a+b)\\[/tex]

Following from above,

25[tex]25x^{2} -16[/tex]

Taking the elements of the expression

[tex]25x^{2} = 5^{2}x^{2}[/tex]

Using the law of indices,

[tex]a^{2} b^{2} = (ab)^{2}[/tex]

[tex]25x^{2} = (5x)^{2}[/tex]

[tex]16 = 4^{2}[/tex]

Therefore,

[tex]25x^{2} -16[/tex] =  [tex](5x)^{2}  - 4^{2}[/tex]

=[tex](5x-4)(5x+4)[/tex]

Hence the correct answer is Option D.

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