To expand the expression [tex]\((c+4)x^4 + (b+c)x^b - 4x^{c+2}\)[/tex], let's proceed step-by-step through the expansion process:
1. Identify the complete expression:
- We start with the polynomial expression: [tex]\((c+4)x^4 + (b+c)x^b - 4x^{c+2}\)[/tex].
2. Distribute each term:
- The first term is [tex]\((c+4)x^4\)[/tex]. Distributing [tex]\(x^4\)[/tex] inside the parenthesis gives us:
[tex]\[
(c+4)x^4 = c \cdot x^4 + 4 \cdot x^4 = c x^4 + 4 x^4
\][/tex]
- The second term is [tex]\((b+c)x^b\)[/tex]. Distributing [tex]\(x^b\)[/tex] inside the parenthesis gives us:
[tex]\[
(b+c)x^b = b \cdot x^b + c \cdot x^b = b x^b + c x^b
\][/tex]
- The third term is [tex]\(-4x^{c+2}\)[/tex], which does not need further expansion as it is already in its simplest form.
3. Combine all parts together:
- Sum all the results we obtained:
[tex]\[
c x^4 + 4 x^4 + b x^b + c x^b - 4 x^{c+2}
\][/tex]
4. Write the final expanded expression:
- Putting all these terms together, we arrive at the expanded expression:
[tex]\[
b x^b + c x^4 + c x^b + 4 x^4 - 4 x^{c+2}
\][/tex]
Therefore, the expanded form of [tex]\((c+4)x^4 + (b+c)x^b - 4x^{c+2}\)[/tex] is:
[tex]\[ b x^b + c x^4 + c x^b + 4 x^4 - 4 x^{c+2} \][/tex]
