How do you evaluate #3(27x^{4}-12x^{2}-6)^{2}-2#?

1 Answer
Jim G.
Nov 15, 2017

#2187x^8-1944x^6-54x^4+432x^2+106#

Explanation:

#"expand "(27x^4-12x^2-6)^2#

#=(27x^4-12x^2-6)(27x^4-12x^2-6)#

#"each term in the second factor is multiplied by"#
#"each term in the first factor"#

#=color(red)(27x^4)(27x^4-12x^2-6)color(red)(-12x^2)(27x^4-12x^2-6)#
#color(white)(=)color(red)(-6)(27x^4-12x^2-6)#

#=729x^8-324x^6-162-324x^6+144x^4+72x^2#
#color(white)(=)-162x^4+72x^2+36#

#=729x^8-648x^6-18x^4+144x^2+36#

#"this expansion is then multiplied by 3"#

#rArr3(729x^8-648x^6-18x^4+144x^2+36)#

#=2187x^8-1944x^6-54x^4+432x^2+108#

#"finally subtract 2"#

#=2187x^8-1944x^6-54x^4+432x^2+106#

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