Question

multiply.
8t⁷(t - t² + 7t³)

8t⁷(t - t² + 7t³) = \square
(simplify your answer.)

Explanation:

Step1: Distribute \(8t^7\) to each term

Use the distributive property \(a(b + c + d)=ab+ac + ad\), here \(a = 8t^7\), \(b=t\), \(c=-t^2\), \(d = 7t^3\).
So we get \(8t^7\times t-8t^7\times t^2 + 8t^7\times7t^3\).

Step2: Apply exponent rule \(a^m\times a^n=a^{m + n}\)

For \(8t^7\times t\): \(t^7\times t=t^{7 + 1}=t^8\), so this term is \(8t^8\).
For \(-8t^7\times t^2\): \(t^7\times t^2=t^{7+2}=t^9\), so this term is \(-8t^9\).
For \(8t^7\times7t^3\): \(8\times7 = 56\) and \(t^7\times t^3=t^{7 + 3}=t^{10}\), so this term is \(56t^{10}\).

Step3: Combine the terms

Putting them together, we have \(8t^8-8t^9 + 56t^{10}\), which can be rewritten as \(56t^{10}-8t^9 + 8t^8\) (by arranging in descending order of exponents).

Answer:

\(56t^{10}-8t^9 + 8t^8\)