Mcguire Simpson
01/09/2024 · Junior High School
b. Expand the product. \( \left(7-z^{2}\right)\left(z^{3}-2 z+2\right)= \)
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Step-by-step Solution
Expand the expression \( (7-z^2)(z^3-2z+2) \)
Simplify the expression by following steps:
- step0: Multiply the terms:
\(\left(7-z^{2}\right)\left(z^{3}-2z+2\right)\)
- step1: Apply the distributive property:
\(7z^{3}-7\times 2z+7\times 2-z^{2}\times z^{3}-\left(-z^{2}\times 2z\right)-z^{2}\times 2\)
- step2: Multiply the numbers:
\(7z^{3}-14z+14-z^{5}-\left(-2z^{3}\right)-2z^{2}\)
- step3: Remove the parentheses:
\(7z^{3}-14z+14-z^{5}+2z^{3}-2z^{2}\)
- step4: Add the terms:
\(9z^{3}-14z+14-z^{5}-2z^{2}\)
Expanding the product \( (7-z^{2})(z^{3}-2z+2) \) gives the result as \( 9z^{3}-14z+14-z^{5}-2z^{2} \).
Quick Answer
\( 9z^{3}-14z+14-z^{5}-2z^{2} \)
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