Question

Factor 25x ^2 + 10x + 1. (25x + 1)(x + 1) (5x + 1)(5x - 1) (5x + 1)²

Answer 1

Answer:

$(5x+1)^2$

Step-by-step explanation:

Factor $25x ^2 + 10x + 1$

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

$5 \cdot 5= 25$

$5+5=10$

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

$25x ^2 + 10x + 1$

$25x ^2 +5x+5x + 1$

Group first two terms and last two terms

$(25x ^2 +5x)+(5x + 1)$

Factor out GCF from each group

$5x(5x+1)+1(5x + 1)$

FActor out 5x+1

$(5x+1)(5x+1)$

$(5x+1)^2$

Answer 2

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