How do you multiply polynomials ?
here is a straight-forward explanation
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Multiplying polynomials is a fundamental concept in algebra. To multiply two polynomials together, you need to follow these steps:
1. Write down the two polynomials that you are multiplying. For example, let's say we are multiplying (3x + 2) and (4x - 7).
2. Multiply each term from the first polynomial by every term from the second polynomial.
- Start with the first term from the first polynomial and multiply it by each term from the second polynomial. In our example, multiply 3x by 4x and by -7.
- Then, move on to the second term in the first polynomial and multiply it by each term from the second polynomial. In our example, multiply 2 by 4x and by -7.
3. Combine all the like terms and simplify the expression if possible.
Let's go through an example to illustrate these steps.
Example: Multiply (3x + 2) and (4x - 7)
Step 1: Write down the two polynomials:
(3x + 2) × (4x - 7)
Step 2: Multiply each term from the first polynomial by each term from the second polynomial:
(3x × 4x) + (3x × -7) + (2 × 4x) + (2 × -7)
Step 3: Simplify the expression:
12x^2 - 21x + 8x - 14
Step 4: Combine the like terms:
12x^2 - 13x - 14
The result is a new polynomial, 12x^2 - 13x - 14.