Question

What is the product of the polynomials 3x2 + 3 and 4x2 - 1?

Answer 1

`12x^4 + 9x^2 - 3\\`

Explanation:

Firstly, put the two equations side by side:

`(3x^2 + 3)(4x^2 - 1)`

The FOIL method is very useful in this scenario, the formula is:

`(a + b)(c + d) = ac + ad + bc + bd`

So plug in the known variables:

`3x^2 * 4x^2 = 12x^4\\3x^2 * -1 = -3x^2\\3 * 4x^2 = 12x^2\\3 * -1 = -3`

`12x^4 - 3x^2 + 12x^2 - 3\\`

This simplifies to:

`12x^4 + 9x^2 - 3\\`

Hope this helps!