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(6n^2-6n-5)(7n^2+6n-5)

3 min read Jun 16, 2024
(6n^2-6n-5)(7n^2+6n-5)

Expanding the Expression (6n^2 - 6n - 5)(7n^2 + 6n - 5)

This expression involves multiplying two trinomials. To expand it, we will use the distributive property (also known as FOIL method).

Here's how to do it:

  1. Multiply the first terms of each trinomial: (6n^2)(7n^2) = 42n^4

  2. Multiply the outer terms: (6n^2)(-5) = -30n^2

  3. Multiply the inner terms: (-6n)(7n^2) = -42n^3

  4. Multiply the last terms: (-6n)(-5) = 30n

  5. Multiply the first term of the first trinomial by the second term of the second trinomial: (6n^2)(6n) = 36n^3

  6. Multiply the first term of the first trinomial by the third term of the second trinomial: (6n^2)(-5) = -30n^2

  7. Multiply the second term of the first trinomial by the first term of the second trinomial: (-6n)(7n^2) = -42n^3

  8. Multiply the second term of the first trinomial by the second term of the second trinomial: (-6n)(6n) = -36n^2

  9. Multiply the second term of the first trinomial by the third term of the second trinomial: (-6n)(-5) = 30n

  10. Multiply the third term of the first trinomial by the first term of the second trinomial: (-5)(7n^2) = -35n^2

  11. Multiply the third term of the first trinomial by the second term of the second trinomial: (-5)(6n) = -30n

  12. Multiply the third term of the first trinomial by the third term of the second trinomial: (-5)(-5) = 25

Now, add all the terms together and combine like terms:

42n^4 - 30n^2 - 42n^3 + 30n + 36n^3 - 30n^2 - 42n^3 - 36n^2 + 30n - 35n^2 - 30n + 25

Simplifying the expression:

42n^4 - 48n^3 - 131n^2 + 25

Therefore, the expanded form of (6n^2 - 6n - 5)(7n^2 + 6n - 5) is 42n^4 - 48n^3 - 131n^2 + 25.

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