Question

What is the product of the polynomials 3x^2 +3 and 4x^2 − 1?

Enter your answer in simplest form in the boxes.

NCVA please help

Answer 1

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

Explanation:

In order to find the product of the polynomials 3x² + 3 and 4x² - 1, we can use the distributive property to multiply each term in the first polynomial by each term in the second polynomial.

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

Use the distributive property to multiply each term in the first polynomial by each term in the second polynomial:

`\sf (3x^2 \cdot 4x^2) + (3x^2 \cdot (-1)) + (3 \cdot 4x^2) + (3 \cdot (-1)`

Now, perform the multiplications:

`\sf 3x^2 \cdot 4x^2 = 12x^4`

`\sf 3x^2 \cdot (-1) = -3x^2`

`\sf 3 \cdot 4x^2 = 12x^2`

`\sf 3 \cdot (-1) = -3`

Now, combine the like terms:

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

Combine the terms with the same exponent:

`\sf 12x^4 + (12x^2 - 3x^2) - 3`

Now, simplify further by combining like terms:

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

So, the product of 3x² + 3 and 4x² - 1 is:

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