Answer
One method that can be used is the First Outside Inside Last (FOIL) method.
Another option is multiplying the binomial by itself.
Work Step by Step
FOIL:
$(5x+1)(5x+1)$
First: $5x*5x$
Outside: $5x*1$
Inside: $5x*1$
Last: $1*1$
$5x*5x+5x*1+5x*1+1*1$
$25x^2+5x+5x+1$
$25x^2+10x+1$
Binomial by itself:
$(5x+1)^2$
$(5x)^2+2*(5x)(1)+(1)^2$
$25x^2+10x+1$
