How do you write # (2x^2 - 5x + 4) ^2 in standard form?

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How do you write # (2x^2 - 5x + 4) ^2 in standard form?

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Answer 1 · 2017-05-18T16:16:14

$4 x^{4} - 20 x^{3} - 41 x^{2} - 40 x + 16$ $4x^4-20x^3-41x^2-40x+16$

Explanation:

$(2 x^{2} - 5 x + 4) (2 x^{2} - 5 x + 4)$ $color(blue)((2x^2-5x+4))color(green)((2x^2-5x+4))$

Multiply everything inside the right bracket by everything in the left.

$- 2 x^{2} (2 x^{2} - 5 x + 4) \to 4 x^{4} - 10 x^{3} + 8 x^{2}$ $color(blue)(color(white)(-)2x^2)color(green)((2x^2-5x+4)) -> 4x^4-10x^3+8x^2$
$. - 5 x (2 x^{2} - 5 x + 4) \to - 10 x^{3} + 25 x^{2} - 20 x$ $color(white)(.)color(blue)(-5x)color(green)((2x^2-5x+4)) ->" "-10x^3+25x^2-20x$
$color(white)(..)color(blue)(+4)color(green)((2x^2-5x+4)) ->ul(" "+8x^2-20x+16)$
$" "4x^4-20x^3-41x^2-40x+16$

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How do you write # (2x^2 - 5x + 4) ^2 in standard form?

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