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What is the standard form of $y = (2 x - 9) (x - 5) - {(2 x + 7)}^{2}$ $y= (2x-9)(x-5)-(2x+7)^2$ ?

1 Answer

Dec 10, 2015

$y = - 2 x^{2} - 47 x - 4$ $y=-2x^2-47x-4$

Explanation:

The general standard form for a quadratic is
$XXX y = a x^{2} + b x + c$ $color(white)("XXX")y=ax^2+bx+c$
with constants $a, b, c$ $a, b, c$

Given
$XXX y = (2 x - 9) (x - 5) - {(2 x + 7)}^{2}$ $color(white)("XXX")y=color(red)((2x-9)(x-5))-color(blue)((2x+7)^2)$

Expanding the terms:
$XXX y = (2 x^{2} - 19 x + 45) - (4 x^{2} + 28 x + 49)$ $color(white)("XXX")y=color(red)((2x^2-19x+45))-color(blue)((4x^2+28x+49))$

Combine like terms:
$XXX y = - 2 x^{2} - 47 x - 4$ $color(white)("XXX")y=-2x^2-47x-4$

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