How do I factor these?

Tak x as a common factor from the first and third term

x(2t+1)+10t+5 now take 5 out as a common factor

x(2t+1)+5(2t+1) now take (2t+1) out as a common factor

(2t+1)(x+5)

r^2-2r+1 is (r-1)^2 so

(r-1)^2-4s^2 difference of two squares

((r-1)-2s)((r-1)+2s))

2xt + 10t + x + 5 factor out 2t from first two terms

2t(x + 5) + x + 5 fact out (x + 5)

(x+5) ( 2t + 1)

r^2 - 2r+ 1 -4s^2 factor out r from first two terms

r ( r-1) second two terms is third binomial formula

1 -4s^2 = (1 + 2s)(1 - 2s)

all together

r ( r-1) + (1 + 2s)(1 - 2s)

2xt + 10t + x + 5

= (2xt+x)+(10t+5)

= x(2t+1) + 5(2t+1)

= (x+5)(2t+1)

r^2 - 2r+ 1 -4s^2

= (r-1)^2 - (2s)^2

= (r-1+2s)(r-1-2s)

2t (x + 5) + (x + 5) = (x + 5)(2t + 1)

(r - 1)² - 4s² = [ (r - 1) - 2s ] [ (r - 1) + 2s ]

2t(x+5)+1(x+5)=(2t+1)(x+5)

r(r-2)+(1-2s)(1+2s)

first one is (x+s)(2t+1)

not sure about the second one