contestada

Factor completely.
27u⁶-8v⁶
a. (3u²-2v²)(9u⁴+6u²v²+4v⁴)
b. (3u²+2v²)(9u⁴+6u²v²+4v⁴)
c. (3u²+2v²)(9u⁴-6u²v²+4v⁴)
d. Prime

Respuesta :

MisterBrian

Answer:

A: (3u²-2v²)(9u⁴+6u²v²+4v⁴)

Step-by-step explanation:

Expression is a combination of terms separated by signs,such as +,-, and so on.

Given expression:

27u⁶-8v⁶

We know:

  • 27 = 3³
  • 8 = 2³

Hence,

  • 3³*u⁶ - 2³*v⁶

Also,

  • u⁶ = (u²)³
  • v⁶ = (v²)³

Hence

  • 3³*(u²)³ - 2³(v²)³

Enclosing the terms within a single parenthesis since each term is now raised by power of 3:

  • (3u²)³ - (2v²)³

We are familiar with this formula:

  • a³-b³ = (a-b)(a²+ab+b²)

Considering a = 3u²

b = 2v²

  • (3u²)³ - (2v²)³ = (3u²-2v²){(3u²)² + (3u²)(2v²) + (2v²)²

= (3v²-2v²)(9u⁴ + 6u²v² + 4v⁴)[Expand each term]

Option A is accurate.

Otras preguntas