How do you simplify #2x ( 6x - 5) - ( 4x - 7x ^ { 2} )#?

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Answer 1 · 2018-01-08T12:29:04

See a solution process below:

First, expand the term on the left by multiplying each term within the parenthesis by the term outside the parenthesis:

#color(red)(2x)(6x - 5) - (4x - 7x^2) =>#

#(color(red)(2x) xx 6x) - (color(red)(2x) xx 5) - (4x - 7x^2) =>#

#12x^2 - 10x - (4x - 7x^2)#

Next, remove the terms on the right from parenthesis. Be careful to handle the signs of each individual term correctly:

#12x^2 - 10x - 4x + 7x^2#

Then, group like terms:

#12x^2 + 7x^2 - 10x - 4x#

Now, combine like terms:

#(12 + 7)x^2 + (-10 - 4)x =>#

#19x^2 + (-14)x =>#

#19x^2 - 14x#

Answer 2 · 2018-01-08T12:44:48

#color(black)(19x^2-14x)#

First: Expand the bracket

#color(red)(2x)(color(blue)(6x) - color(green)(5)) #

#color(red)(2x)*color(blue)(6x)=color(orange)(12x^2)#

#color(red)(2x)*color(green)(-5)=color(orange)(-10x)#

This then leaves us with:

#color(green)(12x^2-10x-(4x-7x^2)#

Since #-1*-1# turns to a #+1#

#-7x^2# turns to a #7x^2# giving us:

#color(orange)(12x^2-10x-4x+7x^2#

Collecting like terms gives us:

#=> color(blue)(19x^2-14x#

Graph Below

graph{19x^2-14x [-3, 6.48, -2.9 1.5]}