Santiago Stephens
07/17/2024 · Elementary School
Multiply the following polynomials. \[ \begin{array}{l}\text { 36. }\left(2 y^{3}-3 y^{2}-y+1\right)(2 y-1)\end{array} \]
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Step-by-step Solution
Calculate or simplify the expression \( (2y^3-3y^2-y+1)(2y-1) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(2y^{3}-3y^{2}-y+1\right)\left(2y-1\right)\)
- step1: Multiply the expression:
\(\left(y^{2}-y-1\right)\left(2y-1\right)^{2}\)
- step2: Rearrange the terms:
\(\left(2y-1\right)^{2}\left(y^{2}-y-1\right)\)
- step3: Expand the expression:
\(\left(4y^{2}-4y+1\right)\left(y^{2}-y-1\right)\)
- step4: Apply the distributive property:
\(4y^{2}\times y^{2}-4y^{2}\times y-4y^{2}\times 1-4y\times y^{2}-\left(-4y\times y\right)-\left(-4y\times 1\right)+1\times y^{2}-1\times y-1\times 1\)
- step5: Multiply the terms:
\(4y^{4}-4y^{3}-4y^{2}-4y^{3}-\left(-4y^{2}\right)-\left(-4y\right)+y^{2}-y-1\)
- step6: Remove the parentheses:
\(4y^{4}-4y^{3}-4y^{2}-4y^{3}+4y^{2}+4y+y^{2}-y-1\)
- step7: Subtract the terms:
\(4y^{4}-8y^{3}+y^{2}+3y-1\)
The product of the given polynomials is \(4y^{4}-8y^{3}+y^{2}+3y-1\).
Quick Answer
\(4y^{4}-8y^{3}+y^{2}+3y-1\)
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