Final answer:
The student's question involves multiplying polynomials and possibly expressing large or small results in scientific notation. The process includes multiplying each term of the first polynomial by each term of the second polynomial, combining like terms, and converting to scientific notation if necessary.
Step-by-step explanation:
The question involves finding the product of two expressions and presenting the answer in the standard form or scientific notation. In mathematics, specifically in algebra, when multiplying polynomials, we use the distributive property to multiply each term of the first polynomial by each term of the second polynomial. Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It is typically used in sciences to handle large and small measurements efficiently.
To find the product, we proceed as follows:
- Multiply each term in the first expression by each term in the second expression.
- Combine like terms, which involves grouping the terms with the same powers of x and simplifying.
- Convert any resulting large or small numbers into scientific notation by moving the decimal place to the right or left and adjusting the exponent on the 10 accordingly.
For example:
(3x + 2x - 1)(24 - 2x + 3) would be expanded to get the product and then expressed possibly in scientific notation, if large or small values result after simplification.
As for scientific notation, a quick example would be multiplying:
(6.022 × 10²³)(6.42 × 10⁻²)
First, we multiply the coefficients (6.022 and 6.42) and then add the exponents of the base 10 (23 and -2), resulting in:
1.67 × 10¹