What is the standard form of $y = (x - 7) (3 x - 5) - {(x + 7)}^{2}$ $y= (x-7)(3x-5)-(x+7)^2$ ?

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Answer 1 · 2015-11-16T22:59:47

So the standard form is $a x^{2} + b x + c$ $ax^2 +bx + c$

$color(red)(underline("You asked for 'standard' form"))$

Consider the first part:
$(x-7)(3x-5)-> 3x^2 - 5x -21x+35 = 3x^2 -26x+35$

Consider the second part:
$(x-7)^2 -> x^2 -14x +49$

Put them together and we end up with:

$y=(3x^2 -26x+35)-( x^2-14x+49)$

The minus sign outside the brackets reverses all the signs within.

$y=3x^2 -26x+35- x^2+14x-49$

$color(brown)(y=2x^2-12x-14)$

$color(blue)("So the standard form is" color(white)(xx) ax^2 +bx + c)$