Question
multiply \left(7x^{2}-6x+5\right)\left(4x^{2}+6x-3\right)
Answers
GPT 3.5
To multiply these two polynomials, we need to use the distributive property multiple times.
We start by multiplying each term in the first polynomial by each term in the second polynomial:
(7x^2) * (4x^2) + (7x^2) * (6x) + (7x^2) * (-3) + (-6x) * (4x^2) + (-6x) * (6x) + (-6x) * (-3) + (5) * (4x^2) + (5) * (6x) + (5) * (-3)
Now, simplify each of these products:
28x^4 + 42x^3 - 21x^2 - 24x^3 - 36x^2 + 18x + 20x^2 + 30x - 15
Finally, combine like terms to get the final answer:
28x^4 + 18x^3 - 5x^2 + 48x - 15
We start by multiplying each term in the first polynomial by each term in the second polynomial:
(7x^2) * (4x^2) + (7x^2) * (6x) + (7x^2) * (-3) + (-6x) * (4x^2) + (-6x) * (6x) + (-6x) * (-3) + (5) * (4x^2) + (5) * (6x) + (5) * (-3)
Now, simplify each of these products:
28x^4 + 42x^3 - 21x^2 - 24x^3 - 36x^2 + 18x + 20x^2 + 30x - 15
Finally, combine like terms to get the final answer:
28x^4 + 18x^3 - 5x^2 + 48x - 15