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(6m^2-8mn+4n^2)(8m+8n)

less than a minute read Jun 16, 2024
(6m^2-8mn+4n^2)(8m+8n)

Simplifying the Expression (6m^2 - 8mn + 4n^2)(8m + 8n)

This expression involves multiplying a trinomial (6m^2 - 8mn + 4n^2) by a binomial (8m + 8n). We can simplify it using the distributive property.

Here's how:

  1. Distribute the first term of the binomial: (8m)(6m^2 - 8mn + 4n^2) = 48m^3 - 64m^2n + 32mn^2

  2. Distribute the second term of the binomial: (8n)(6m^2 - 8mn + 4n^2) = 48m^2n - 64mn^2 + 32n^3

  3. Combine the results from steps 1 and 2: 48m^3 - 64m^2n + 32mn^2 + 48m^2n - 64mn^2 + 32n^3

  4. Simplify by combining like terms: 48m^3 - 16m^2n - 32mn^2 + 32n^3

Therefore, the simplified form of the expression (6m^2 - 8mn + 4n^2)(8m + 8n) is 48m^3 - 16m^2n - 32mn^2 + 32n^3.

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