To find the product of the two polynomials \((3x^2 - 8)(4x^2 + 7)\), we can use the distributive property (also known as the FOIL method for binomials).
We will multiply each term in the first polynomial by each term in the second polynomial:
-
Multiply the first terms: \[ 3x^2 \cdot 4x^2 = 12x^4 \]
-
Multiply the outer terms: \[ 3x^2 \cdot 7 = 21x^2 \]
-
Multiply the inner terms: \[ -8 \cdot 4x^2 = -32x^2 \]
-
Multiply the last terms: \[ -8 \cdot 7 = -56 \]
Now, we combine all these products together: \[ 12x^4 + 21x^2 - 32x^2 - 56 \]
Next, we will combine the like terms: \[ 21x^2 - 32x^2 = -11x^2 \]
So the expression simplifies to: \[ 12x^4 - 11x^2 - 56 \]
Finally, in descending order of exponents, the product is: \[ \boxed{12x^4 - 11x^2 - 56} \]
1 answer