MATH SOLVE

4 months ago

Q:
# Which of the following expressions is equal to 3x^2+27

Accepted Solution

A:

Factor:

3x^2 + 27

= 3(x^2 + 9)

Answer is 3(x^2 + 9), when factored.

A) (3x + 9i)(x + 3i)

= (3x + 9i)(x + 3i)

= (3x)(x) + (3x)(3i) + (9i)(x) + (9i)(3i)

= 3x^2 + 9ix + 9ix + 27i^2

= 27i^2 + 18ix + 3x^2

B) (3x - 9i)(x + 3i)

= (3x + - 9i)(x + 3i)

= (3x)(x) + (3x)(3i) + ( - 9i)(x) + (- 9i)(3i)

= 3x^2 + 9ix - 9ix - 27i^2

= 27i^2 + 3x^2

C) (3x - 6i)(x + 21i)

= (3x + - 6i)(x + 21i)

= (3x)(x) + (3x)(21i) + (- 6i)(x) + ( -6i)(21i)

= 3x^2 + 63ix - 6ix - 126i^2

= - 126i^2 + 57ix + 3x^2

D) (3x - 9i)(x - 3i)

= (3x + - 9)(x + - 3)

= (3x)(x) + (3x)( - 3i) + (- 9)(x) + ( - 9)( - 3i)

= 3x^2 - 9ix - 9x + 27i

= 9ix + 3x^2 + 27i - 9x

Hope that helps!!!

3x^2 + 27

= 3(x^2 + 9)

Answer is 3(x^2 + 9), when factored.

A) (3x + 9i)(x + 3i)

= (3x + 9i)(x + 3i)

= (3x)(x) + (3x)(3i) + (9i)(x) + (9i)(3i)

= 3x^2 + 9ix + 9ix + 27i^2

= 27i^2 + 18ix + 3x^2

B) (3x - 9i)(x + 3i)

= (3x + - 9i)(x + 3i)

= (3x)(x) + (3x)(3i) + ( - 9i)(x) + (- 9i)(3i)

= 3x^2 + 9ix - 9ix - 27i^2

= 27i^2 + 3x^2

C) (3x - 6i)(x + 21i)

= (3x + - 6i)(x + 21i)

= (3x)(x) + (3x)(21i) + (- 6i)(x) + ( -6i)(21i)

= 3x^2 + 63ix - 6ix - 126i^2

= - 126i^2 + 57ix + 3x^2

D) (3x - 9i)(x - 3i)

= (3x + - 9)(x + - 3)

= (3x)(x) + (3x)( - 3i) + (- 9)(x) + ( - 9)( - 3i)

= 3x^2 - 9ix - 9x + 27i

= 9ix + 3x^2 + 27i - 9x

Hope that helps!!!