Question

If c(x)= 4x^3-5x^2+2 and d(x)= 3x^2+ 6x-10, find each value

Equation: 6c(4a)+2d(3a-5)

Answer 1

6 c(4a) is short hand for
replace x with (4a) in the expression
4x^3-5x^2+2

(everywhere you see x, put in (4a) instead)

then
multiply every term by 6

that gives you 6 c(4a)

use the same idea for 2 d(3a-5)
where
d(x) is 3x^2+ 6x-10

Can you do that?

Answer 2

I did it the way you said but didnt come up to the answer in the book

Answer 3

not too surprising, it looks messy. what did you get for just
c(4a) ?

Answer 4

96a^3-120a^2+12

Answer 5

that is not c(4a)

Answer 6

replace x with (4a) in the expression
4x^3-5x^2+2

Answer 7

I did and i got 16a^3-20a^2+2. Then i multiplied everything by 6 like you said :o

Answer 8

ok, first when you replace x with 4a in
4* x^3 you write it like this: 4* (4a)^3
remember that x^3 is short-hand for x*x*x (x times itself 3 times)
so the answer with 4a instead of x is 4* (4a)*(4a)*(4a)
you do not get 16a^3

can you retry?

Answer 9

256^3-80a^2+2?

Answer 10

you would reorder 4* (4a)*(4a)*(4a) = 4*4*a*4*a*4*a as
4*4*4*4 * a*a*a
or using short-hand (exponents)
4^4 * a^3
or
256 a^3

Answer 11

256^3-80a^2+2?

yes, assuming you left out an a in there. now multiply by 6
6(256a^3 -80a^2 +2)

Answer 12

I get
1536 a^3 -480 a^2 +12

now the ugly one
d(3a-5)
where
3x^2+ 6x-10

if we just replace x with (3a-5) we get
3*(3a-5)^2 +6(3a-5) -10
can you simplify this?

Answer 13

27a^2+18a-115?

Answer 14

27 a^2 -72a +35

Answer 15

what did you get for (3a-5)^2 ?
(3a-5)(3a-5)= 9a^2 -15a -15a +25
9a^2 -30a+25
we want 3*(3a-5)^2 so mult by 3:
27a^2 -90a +75

Answer 16

can you finish by adding in +6(3a-5) -10