Questions: Multiply and simplify: 5z(2z+5)(z-1) 10z^3+5z

Multiply and simplify: 5z(2z+5)(z-1) 10z^3+5z
Transcript text: Multiply and simplify: \[ \begin{array}{l} 5 z(2 z+5)(z-1) \\ 10 z^{3}+5 z \end{array} \]
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Solution

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Solution Steps

To solve the problem of multiplying and simplifying the given expression, follow these steps:

  1. Distribute the terms in the expression 5z(2z+5)(z−1)5z(2z+5)(z-1).
  2. Simplify the resulting polynomial by combining like terms.
Step 1: Distribute the Terms

Start with the expression 5z(2z+5)(z−1)5z(2z+5)(z-1). Distribute 5z5z across the terms (2z+5)(2z+5) and (z−1)(z-1).

Step 2: Expand the Expression

First, expand (2z+5)(z−1)(2z+5)(z-1):

(2z+5)(z−1)=2z2−2z+5z−5=2z2+3z−5 (2z+5)(z-1) = 2z^2 - 2z + 5z - 5 = 2z^2 + 3z - 5

Now, multiply the result by 5z5z:

5z(2z2+3z−5)=10z3+15z2−25z 5z(2z^2 + 3z - 5) = 10z^3 + 15z^2 - 25z

Final Answer

The simplified expression is:

10z3+15z2−25z \boxed{10z^3 + 15z^2 - 25z}

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