How do you factor #25x^2 + 10x + 1#?

1 Answer
smendyka
Dec 8, 2017

See a solution process below:

Explanation:

Use this rule of quadratics to factor the expression:

#color(red)(a)^2 + 2color(red)(a)color(blue)(b) + color(blue)(b)^2 = (color(red)(a) + color(blue)(b))(color(red)(a) + color(blue)(b)) = (color(red)(a) + color(blue)(b))^2#

Let #color(red)(a)^2 = 25x^2# then #color(red)(a) = sqrt(25x^2) = 5x#

Let #color(blue)(b)^2 = 1# then #color(blue)(b) = sqrt(1^2) = 1#

Substituting gives:

#25x^2 + 10x + 1 =>#

#(color(red)(5x))^2 + (2 * color(red)(5x) * color(blue)(1)) + color(blue)(1)^2 =>#

#(color(red)(5x) + color(blue)(1))(color(red)(5x) + color(blue)(1)) =>#

#(color(red)(5x) + color(blue)(1))^2#

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