Respuesta :

JonHenderson55
The correct answer is:  [C]:  " (5x + 1)² " .
______________________________________
Explanation:
______________________________________
Choice [A] is incorrect: "(25x+1)(x+1) = 25x² +25x +1x +1 = 25x² + 26x + 1 .
______________________________________
Choice [B] is incorrect: "(5x+1)(5x-1)= 25x² -5x+5x -1 = 25x² - 1 .
______________________________________
This leaves us with:  Answer choice:  [C]:  " (5x + 1)² "  ;
                                                       →   as the correct answer.
__________________________________________________
However, let us work through this answer choice:
__________________________________________________
  (5x + 1)² = (5x + 1)(5x + 1) = 25x² + 5x + 5x + 1 ;
                                             = 25x²  + 10x + 1 ; which is the
                                                    expression provided in question;
___________________________________________________
So the correct answer is:  [C]:  " (5x + 1)² " .
___________________________________________________

Answer:

[tex](5x+1)^2[/tex]

Step-by-step explanation:

Factor [tex]25x ^2 + 10x + 1[/tex]

To factor this expression we use AC method. multiply 'a' and 'c'

Given expression is ax^2+bx+c

'a' times 'c' is 25 times 1 = 25

Now product is 25 and sum is the coefficient of middle term is 10

[tex]5 \cdot 5= 25[/tex]

[tex]5+5=10[/tex]

Now break the middle term 10x using factors 5 and 5

[tex]25x ^2 + 10x + 1[/tex]

[tex]25x ^2 +5x+5x + 1[/tex]

Group first two terms and last two terms

[tex](25x ^2 +5x)+(5x + 1)[/tex]

Factor out GCF from each group

[tex]5x(5x+1)+1(5x + 1)[/tex]

FActor out 5x+1

[tex](5x+1)(5x+1)[/tex]

[tex](5x+1)^2[/tex]

Otras preguntas