How do you simplify the expression ${(5 x - 2)}^{2}$ $(5x-2)^2$ ?

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How do you simplify the expression ${(5 x - 2)}^{2}$ $(5x-2)^2$ ?

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Answer 1 · 2017-06-17T15:57:10

$25 x^{2} - 20 x + 4$ $25x^2-20x+4$

Explanation:

To solve this problem first you rewrite as follows:

$(5 x - 2) (5 x - 2)$ $(color(blue)(5x)color(darkred)(-2))(color(red)(5x)color(green)(-2))$

Then you proceed to FOIL it:

Where you multiply the $first term$ $color(blue)"first term"$ with the $outer term$ $color(red)"outer term"$ then you multiply the $first term$ $color(blue)"first term"$ with the $inner term$ $color(green)"inner term"$ :

$(5 x) (5 x) = 25 x^{2}$ $(color(blue)(5x))(color(red)(5x))=25x^2$

$(5 x) (- 2) = - 10 x$ $(color(blue)(5x))(color(green)(-2))=-10x$

Now you multiply the $last term$ $color(darkred)"last term"$ with the $outer term$ $color(red)"outer term"$ then you multiply the $last term$ $color(darkred)"last term"$ with the $inner term$ $color(green)"inner term"$ :

$(- 2) (5 x) = - 10 x$ $color(darkred)((-2))(color(red)(5x))=-10x$

$(- 2) (- 2) = 4$ $color(darkred)((-2))(color(green)(-2))=4$

Now combine them:

$25 x^{2} - 10 x - 10 x + 4$ $25x^2-10x-10x+4$

Simplify:

$25 x^{2} - 20 x + 4$ $25x^2-20x+4$

Answer 2 · 2017-06-17T18:33:22

$25 x^{2} - 20 x + 4$ $25x^2-20x+4$

Explanation:

$express {(5 x - 2)}^{2} as (5 x - 2) (5 x - 2)$ $"express " (5x-2)^2" as " (5x-2)(5x-2)$

$each term in the second bracket is multiplied by each term in$ $"each term in the second bracket is multiplied by each term in"$
$the first bracket$ $"the first bracket"$

$(5 x - 2) (5 x - 2)$ $(color(red)(5x-2))(5x-2)$

$= 5 x (5 x - 2) - 2 (5 x - 2)$ $=color(red)(5x)(5x-2)color(red)(-2)(5x-2)$

$= (5 x \times 5 x) + (5 x \times - 2) + (- 2 \times 5 x) + (- 2 \times - 2)$ $=(color(red)(5x)xx5x)+(color(red)(5x)xx-2)+(color(red)(-2)xx5x)+(color(red)(-2)xx-2)$

$= 25 x^{2} + (- 10 x) + (- 10 x) + 4$ $=25x^2+(-10x)+(-10x)+4$

$= 25 x^{2} - 10 x - 10 x + 4$ $=25x^2-10x-10x+4$

$= 25 x^{2} - 20 x + 4$ $=25x^2-20x+4$

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How do you simplify the expression ${(5 x - 2)}^{2}$ $(5x-2)^2$ ?

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