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

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Answer 1 · 2015-11-16T22:59:47

So the standard form is #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)#