Question

(3x^2-x-7)(2x^2+x+2)

Answer 1

`6x^4 + x^3 -9x^2 -9x + 14`

Explanation:

`(3x^2-x-7)(2x^2 + x+ 2) = \\\\(3x^2)(2x^2) + (3x^2)(x) + (3x^2)(2) + (-x)(2x^2) + (-x)(x) + (-x)(2) + (-7)(2x^2) + (-7)(x) + (-7)(-2)\\\\6x^4 + 3x^3 + 6x^2 -2x^3 -x^2 -2x -14x^2 -7x +14\\\\6x^4 + x^3 -9x^2 - 9x +14`

We normally use FOIL to multiply two binomial expressions. In this case we will use an extended version of FOIL to multiply two trinomial expressions. There are three terms and two expressions, so our unsimplified product has 9 terms total. Add like terms and then the answer is in simplest form.