The Correct Answer and Explanation is:
Of course. Here is the correct answer and a detailed explanation.
Correct Answer: -24x³ + 18x² – 3x – 9
Explanation
The problem asks you to multiply two polynomials: (5x – 4x² – 3) and (3 + 6x). The image correctly uses the grid method, also known as the box method, to organize this multiplication. This method ensures that every term in the first polynomial is multiplied by every term in the second one.
The calculations within the grid are all correct:
- -4x² times 3 = -12x²
- -4x² times 6x = -24x³
- 5x times 3 = 15x
- 5x times 6x = 30x²
- -3 times 3 = -9
- -3 times 6x = -18x
The next crucial step is to combine all the terms from the boxes and simplify the expression by combining like terms. Like terms are terms that have the same variable raised to the same power.
First, write out all the products from the grid:
-24x³ – 12x² + 30x² + 15x – 18x – 9
Now, group the like terms together:
- Cubic terms (x³): There is only one term with x³, which is -24x³.
- Quadratic terms (x²): There are two terms, -12x² and +30x². Combining them gives you 30x² – 12x² = 18x².
- Linear terms (x): There are two terms, +15x and -18x. Combining them gives you 15x – 18x = -3x.
- Constant terms: There is only one constant term, which is -9.
Finally, write these simplified terms together in standard form, from the highest power of x to the lowest. This gives you the final answer.
-24x³ + 18x² – 3x – 9
