How do you factor #7x^2-28 #?

2 Answers
Jim G.
Mar 29, 2017

#7(x-2)(x+2)#

Explanation:

There is a #color(blue)"common factor"# of 7 in both terms which can be taken out.

#rArr7(x^2-4)tocolor(red)((1))#

#x^2-4" is a " color(blue)"difference of squares"# which is factorised in general as follows.

#color(red)(bar(ul(|color(white)(2/2)color(black)(a^2-b^2=(a-b)(a+b))color(white)(2/2)|)))#

#"here " a=x" and " b=2#

#rArrx^2-4=(x-2)(x+2)#

going back to #color(red)((1))#

#rArr7x^2-28=7(x-2)(x+2)#

EZ as pi
Mar 29, 2017

#= 7(x+2)(x-2)#

Explanation:

Always look for a common factor first.

It is #7# in this case.

#7x^2 -28 = 7(x^2-4)" "larr# this is the difference of squares.

#= 7(x+2)(x-2)#

The expression has 3 factors

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