if c(x)=x^3-2x and d(x)=4x^2-6x+8, find the value of 3c(a-4)+3d(a+5)

Answer 1

3c(x) + 3d(x)

=3((a-4)^3 -2(a-4)) + 3(4(a+5)^2 -6(a+5)+8))

= 3(a^3 -12a^2 +48a -64 -2a+8) + 3(4a^2 +40a +100) - 18a -30 +48

= 3a^3 -36a^2+12a^2 -6a +24 +144a +120a -18a - 192 +300 +18

= 3a^3 - 24a^2 + 240a +248

c(x) = c(a-4)

= (a-4)^3 -2(a-4)

d(x) = d(a+5)

=4(a+5)^2 - 6(a+5) + 8

replace x by a-4 for c(x)

replace x by a+5 for d(x)

then multiply each by 3

expand

then combine like terms

use the formula (a-b)^3 = a^3 -3a^2b + 3ab^2 -b^3 where b=4 for c(a-4)

and use the formula (a+b)^3 = a^2 +2ab+ b^2 where b=5 for d(a+5)

it's easy to make a mistake in exoanding, in signs or adding like terms

so, no guarantee the above is error free, but if you do it yourself and get the same

answer, odds are good it's right