Final answer:
The student is asking how to multiply two polynomials to obtain a resulting polynomial in standard form. This is achieved through the distributive property, often called the FOIL method for binomials, which involves multiplying each term of one polynomial by every term of the other and combining like terms.
Step-by-step explanation:
The student's question is about expanding and simplifying the product of two polynomials, which is an important concept in algebra. Specifically, the student wants to multiply the polynomials (4x²+x-1)(-3x²-3x-3). To do this, each term of the first polynomial must be multiplied by each term of the second polynomial, and then like terms are combined. This process is known as the distributive property, or FOIL (First, Outer, Inner, Last) method when dealing with binomials. The result will be a polynomial in standard form.
Another provided example includes resolving a quadratic equation using the quadratic formula, which is relevant to the process of solving for the roots of the expanded polynomial equation resulting from the multiplication of two polynomials. Although the student has included unrelated information about quadratic equations and solutions, focusing on the multiplication and combination of terms will address the question at hand.