What is a simpler form of the expression? (2n2 + 5n + 3)(4n - 5) A. 8n^3 + 10n² - 13 n - 15 B. 8n^3 + 30n² - 37n - 15 C. 8n^3 - 10n² + 37n - 15 D. 8n^3+ 13n² - 10n -15
Mathematics · High School · Mon Jan 18 2021
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Given the equation:
(2n^2 + 5n + 3) ( 4n - 5)
Determine the simpler form of the expression.
Solution:
In order to determine the simpler form of the solution we simply needed to apply the FOIL Method. Multiply the first term of the first equation, to the first and last term of the second equation. Then, multiply the last term of the first equation, to the first and last term of the second equation
To clearly see how it works, here's a step by step solution.
= (2n^2)(4n)
=8n^3
First term of the first equation multiplied to the first term of the second equation.
=(2n^2)(-5)
= -10n^2
First term of the first equation multiplied to the last term of the second equation.
=(5n)(4n)
=20n^2
2nd term of the first equation multiplied to the first term of the second equation.
=(5n)(-5)
= -25n
2nd term of the first equation multiplied to the fast term of the second equation.
=(3)(4n)
=12n
Last term of the first equation multiplied to the first term of the second equation.
=(3)(-5)
=-15
Last term of the first equation multiplied to the first term of the second equation.
= 8n^3 - 10n^2 + 20n^2 - 25n + 12n - 15
= 8n^3 + 10 - 13n - 15
Final answer:
= 8n^3 + 10 - 13n - 15