High School

Which statement shows how to find the product of [tex]2x^4(2x^2 + 3x + 4)[/tex]?

A. [tex]2x^8 + 3x^4 + 4x^4[/tex]
B. [tex]4x^6 + 6x^5 + 8x^4[/tex]
C. [tex]4x^4 + 3x^5 + 2x^6[/tex]
D. [tex]3x^6 + 4x^5 + 5x^4[/tex]

Answer :

To find the product of 2x4(2x2 + 3x + 4), we apply the distributive property by multiplying 2x4 across each term in the bracket, resulting in 4x6 + 6x5 + 8x4, which corresponds to option (2).

To find the product of 2x4(2x2 + 3x + 4), you need to distribute the 2x4 across each term in the parenthesis. This process is known as the distributive property.

Here's the distribution step by step:

  • Multiply 2x4 by 2x2 which yields 4x6.
  • Multiply 2x4 by 3x which gives 6x5.
  • Finally, multiply 2x4 by 4 to get 8x4.

Combining these products, we get the final expression: 4x6 + 6x5 + 8x4.

Therefore, the correct statement showing how to find the product is option (2).

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