(7n-2-%2B-6n-%E2%88%92-5).jpeg "(6n 2 − 6n − 5)(7n 2 + 6n − 5)")
Multiplying Binomials: (6n² − 6n − 5)(7n² + 6n − 5)
This problem involves multiplying two trinomials. To solve this, we'll use the distributive property and perform a series of multiplications.
Here's how to approach it:
-
Distribute the first term of the first trinomial:
- (6n²) * (7n² + 6n - 5) = 42n⁴ + 36n³ - 30n²
-
Distribute the second term of the first trinomial:
- (-6n) * (7n² + 6n - 5) = -42n³ - 36n² + 30n
-
Distribute the third term of the first trinomial:
- (-5) * (7n² + 6n - 5) = -35n² - 30n + 25
-
Combine like terms:
- 42n⁴ + 36n³ - 30n² - 42n³ - 36n² + 30n - 35n² - 30n + 25 = 42n⁴ - 6n³ - 101n² + 25
Therefore, the product of (6n² − 6n − 5)(7n² + 6n − 5) is 42n⁴ - 6n³ - 101n² + 25.
Key Points:
- Distributive Property: Remember that when multiplying polynomials, you must multiply each term of one polynomial by every term of the other polynomial.
- Combining Like Terms: After distributing, combine terms that have the same variable and exponent.
- Order of Operations: Remember to follow the order of operations (PEMDAS/BODMAS) when simplifying the expression.