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$(p+q)^4$

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Polynomial vocabulary

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Q.

(p+q)^4

Expand Expression: To find the degree of the polynomial $(p+q)^4$ , we need to expand the expression using the binomial theorem or Pascal's triangle.
Binomial Theorem: The binomial theorem tells us that $(a+b)^n = a^n + \binom{n}{1}a^{(n-1)}b + \binom{n}{2}a^{(n-2)}b^2 + \ldots + b^n$ . Applying this to $(p+q)^4$ , we get: $\newline$ $(p+q)^4 = p^4 + 4p^3q + 6p^2q^2 + 4pq^3 + q^4$ .
Identify Degrees: Now, we identify the degree of each term in the expanded polynomial. $\newline$ Degree of $p^4$ : $4$ $\newline$ Degree of $4p^3q$ : $3 + 1 = 4$ $\newline$ Degree of $6p^2q^2$ : $2 + 2 = 4$ $\newline$ Degree of $4pq^3$ : $1 + 3 = 4$ $\newline$ Degree of $q^4$ : $4$
Degree of Polynomial: Since all terms have the same degree, the degree of the polynomial is $4$ .

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