In STANDARD form express the following product of 2x^2 + 6x - 8 and x + 3. Show your work
To find the product of two binomials, we can use the distributive property. We need to multiply each term in the first binomial by each term in the second binomial.
(2x^2 + 6x - 8)(x + 3)
First, we multiply 2x^2 by x and 2x^2 by 3:
2x^3 + 6x^2
Next, we multiply 6x by x and 6x by 3:
6x^2 + 18x
Finally, we multiply -8 by x and -8 by 3:
-8x - 24
Putting it all together, we have:
2x^3 + 6x^2 + 6x^2 + 18x - 8x - 24
Combining like terms:
2x^3 + 12x^2 + 10x - 24
The product of 2x^2 + 6x - 8 and x + 3 in standard form is 2x^3 + 12x^2 + 10x - 24.