Choose the correct simplification of the expression (8x − 5)(2x2 − 5x − 6).
16x3 − 50x2 − 23x − 30
16x3 − 50x2 − 23x + 30
16x3 − 30x2 − 23x + 30
16x3 + 50x2 − 23x + 30
16x3 - 50x2 - 23x + 30
To simplify the expression (8x − 5)(2x2 − 5x − 6), we need to distribute the first term (8x) to each term in the second expression (2x^2 − 5x − 6) and then combine like terms.
First, distribute the 8x to each term in the second expression:
8x * 2x^2 = 16x^3
8x * (-5x) = -40x^2
8x * (-6) = -48x
Next, distribute the -5 to each term in the second expression:
-5 * 2x^2 = -10x^2
-5 * (-5x) = 25x
-5 * (-6) = 30
Now we can combine like terms:
16x^3 - 40x^2 - 48x - 10x^2 + 25x + 30
Combining like terms, we get:
16x^3 - 50x^2 - 23x + 30
Therefore, the correct simplification of the expression is 16x^3 - 50x^2 - 23x + 30. So the correct answer is:
16x3 − 50x2 − 23x + 30.