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

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1 Answer

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Answer:


\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

User Hassan Fayyaz
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