The product of (-1/2y + 4y^2 - 3)(4y-5) is given to be [32y³-44y²-19y + 30]/30. See the attached graph.
What is the calculation justifying the above?
Step 1 - Combined Multiplied terms into a single fraction
(-1/2y + 4y² - 3) (4y-5)
(-y/2 + 4y² -3) (4y -5)
Step 2 - Find the Common Denominator
(-y/3 + 4y²-3) (4y-5)
[(-y/2 + ((2*4y²)/2) + 2(-3)/2](4y-5)
Step 3 - Combine Fractions with Common Denominator
(-y/2 + (2*4y²)/2 + 2(-3)/2)(4y-5)
(-y (2*4y² + 2(-3)/2)(4y-5)
Step 4 - Multiply the numbers and rearrange the terms, then combine multiplied terms into a single fraction
[(8y² -y-6)(4y-5)]/2
Step 5 - Distribute and Combine like terms
[32y³ - 40y² - 4y²+5y-24y+30] /2
32y³ -44y² +5y-24+30/2
Step 6 - Combine Like terms
32y³ -44y² + 5y-24 + 30/2
32y³ -44y²-19y+30/2
⇒ 32y³ - 44y² -19y + 30/2
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