Question

What is the least common multiple of x^2-16 and x^2+4x-32?

Answer 1

Answer:

• (x - 4)(x + 4)(x + 8)

Step-by-step explanation:

Factorize the given expressions:

• x² - 16 = x² - 4² = (x - 4)(x + 4)
• x² + 4x - 32 = x² + 8x - 4x - 32 = x(x + 8) - 4(x + 8) = (x - 4)(x + 8)

The LCM is the product of all unique  factors of both expressions:

• (x - 4)(x + 4)(x + 8)

Answer 2

The least common multiple is the smallest expression that can be divided by both of the given expressions.

x^2 - 16 = (x - 4)(x + 4)

x^2 + 4x - 32 = (x + 8)(x - 4)

Both of the factored versions of the expressions have an (x - 4) in them. Thus, that will automatically be included in the LCM. Next, we have to include the (x + 4) and the (x + 8) in our LCM.

LCM = (x - 4)(x + 4)(x + 8)

Hope this helps! :)