How do you evaluate #(x - 7) ( x ^ { 2} + 2x + 6)#?

1 Answer
Jim G.
Nov 1, 2017

#x^3-5x^2-8x-42#

Explanation:

#"each term in the second bracket must be multiplied"#
#"by each term in the first bracket"#

#rArr(color(red)(x-7))(x^2+2x+6)#

#=color(red)(x)(x^2+2x+6)color(red)(-7)(x^2+2x+6)#

#=(color(red)(x)xx x^2)+(color(red)(x)xx2x)+(color(red)(x)xx6)#

#color(white)(=)+(color(red)(-7)xx x^2)+(color(red)(-7)xx2x)+(color(red)(-7)xx6)#

#=x^3+2x^2+6x-7x^2-14x-42larrcolor(blue)"collect like terms"#

#=x^3-5x^2-8x-42#

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