How do you simplify (5-2x)^2(5−2x)2?

1 Answer
smendyka
Jun 14, 2018

See a solution process below:

Explanation:

For this special case of quadratics we can use this rule to expand and simplify this expression:

(color(red)(x) - color(blue)(y))^2 = (color(red)(x) - color(blue)(y))(color(red)(x) - color(blue)(y)) = color(red)(x)^2 - 2color(red)(x)color(blue)(y) + color(blue)(y)^2(x−y)2=(x−y)(x−y)=x2−2xy+y2

Substituting the values from the problem gives:

(color(red)(5) - color(blue)(2x))^2 =>(5−2x)2⇒

(color(red)(5) - color(blue)(2x))(color(red)(5) - color(blue)(2x)) =>(5−2x)(5−2x)⇒

color(red)(5)^2 - (2 * color(red)(5) * color(blue)(2x)) + color(blue)((2x))^2 =>52−(2⋅5⋅2x)+(2x)2⇒

25 - 20x + 4x^225−20x+4x2

Or, in standard form:

4x^2 - 20x + 254x2−20x+25

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