Question

What is a simpler form of the expression?

(2n^2 + 5n +3)(4n - 5)

Answer 1

`\large\boxed{(2n^2+5n+3)(4n-5)=8n^3+10n^2-13n-15}`

Explanation:

`\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(2n^2+5n+3)(4n-5)\\\\=(2n^2)(4n)+(2n^2)(-5)+(5n)(4n)+(5n)(-5)+(3)(4n)+(3)(-5)\\\\=8n^3-10n^2+20n^2-25n+12n-15\\\\\text{combine like terms}\\\\=8n^3+(-10n^2+20n^2)+(-25n+12n)-15\\\\=8n^3+10n^2-13n-15`

Answer 2

8n³ + 10n² - 13n - 15

Explanation:

Distribute the factors by multiplying each term in the first factor by each term in the second factor, that is

4n(2n² + 5n + 3) - 5(2n² + 5n + 3) ← distribute both parenthesis

= 8n³ + 20n² + 12n - 10n² - 25n - 15 ← collect like terms

= 8n³ + 10n² - 13n - 15