Question

multiply the polynomials and simplify.\\((2b^3 - b^2)(a^4b + 5 + a^4b^2)\\)\
show your work here\
hint: to add an exponent (\\(x^y\\)), type \exponent\ or press \^\\
enter your answer

Explanation:

Step1: Distribute \(2b^3\)

Multiply \(2b^3\) by each term in the second polynomial:
\(2b^3 \cdot a^4b = 2a^4b^{4}\), \(2b^3 \cdot 5 = 10b^3\), \(2b^3 \cdot a^4b^2 = 2a^4b^{5}\)

Step2: Distribute \(-b^2\)

Multiply \(-b^2\) by each term in the second polynomial:
\(-b^2 \cdot a^4b = -a^4b^{3}\), \(-b^2 \cdot 5 = -5b^2\), \(-b^2 \cdot a^4b^2 = -a^4b^{4}\)

Step3: Combine like terms

• For \(a^4b^4\): \(2a^4b^4 - a^4b^4 = a^4b^4\)
• For \(a^4b^5\): \(2a^4b^5\) (no like terms)
• For \(a^4b^3\): \(-a^4b^3\) (no like terms)
• For \(b^3\): \(10b^3\) (no like terms)
• For \(b^2\): \(-5b^2\) (no like terms)

Answer:

\(2a^4b^5 + a^4b^4 - a^4b^3 + 10b^3 - 5b^2\)