When (5k+1)^2 is divided by 5,the remainder i | vedclass

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Question

(A) To find the remainder when $(5k+1)^2$ is divided by $5$,we expand the expression using the identity $(a+b)^2 = a^2 + 2ab + b^2$.$(5k+1)^2 = (5k)^2

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) To find the remainder when $(5k+1)^2$ is divided by $5$,we expand the expression using the identity $(a+b)^2 = a^2 + 2ab + b^2$.$(5k+1)^2 = (5k)^2 + 2(5k)(1) + (1)^2$$= 25k^2 + 10k + 1$Now,we can rewrite this expression as:$= 5(5k^2 + 2k) + 1$Since $5(5k^2 + 2k)$ is clearly divisible by $5$,the remainder when the entire expression is divided by $5$ is $1$.

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