Question

p(a) = a^3-5; Find p(x-4)

Answer 1

\[p(a) = a^3-5\]
to find \(p(x-4)\), replace \(a\) with \((x-4)\).

Answer 2

\[\large p \left( x-4 \right)=\color{green}{\left( x-4 \right)^3-5}\] ... and Simplify...

Answer 3

I understand that, but what would the simplified solution be? and thank you.

Answer 4

do you know what \((a-b)^3\) looks like expanded?

Answer 5

no

Answer 6

how about \((a-b)^2\) ?

Answer 7

a^2+ 2ab+b^2 ??

Answer 8

almost.. \[a^2- 2ab+b^2 \]

Answer 9

alright

Answer 10

\[(a-b)^3 \\=(a-b)^1(a-b)^2 \\ = (a-b)(a^2-2ab+b^2)\\=a(a^2-2ab+b^2)-b(a^2-2ab+b^2)\]

Answer 11

\[(a-b)^3 \\=(a-b)^1(a-b)^2 \\ = (a-b)(a^2-2ab+b^2)\\=a(a^2-2ab+b^2)-b(a^2-2ab+b^2)\\=a^3-2a^b+ab^2 \ -a^2b+2ab^2-b^3\]

Answer 12

\[=a^3-3a^2b+3ab^2-b^3\]

Answer 13

so \[(x-4)^3\\=x^3-3x^2\cdot4+3x \cdot4^2-4^3\\=\Large x^3-12x^2+48x-64\]

Answer 14

\[p(x-4)\\=(x-4)^3-5\\= \left[ x^3-12x^2+48x-64 \right]-5\\=\color{green}{x^3-12x^2+48x-69}\]

Answer 15

thank you so much