Question

Need help in these to math problems

15. Factor out the greatest common factor.
30t2u + 12tu2 + 24tu

A. 3tu(10t + 4u + 8)

B. 6u(5t – 2u + 4)

C. 6tu(5t + 2u + 4)

D. 2tu(15t + 6u + 12)






16. Complete the property of exponents. bn ⋅ bm = _______.

A. bn+m

B. bn ⋅ m

C. bn – m

D. bn + bm

Answer 1

Question 1:

For this case we have that by definition, the GCF of two numbers is the largest number that is a factor of both numbers. For example, the number 10 is the biggest factor that 50 and 30 have in common.

We must find the GCF of the following expression:

`30t ^ 2u + 12tu ^ 2 + 24tu`

We look for the prime factorization of each number:

`30: 2 * 3 * 5\\12: 2 * 2 * 3\\24: 2 * 2 * 2 * 3`

The GCF of the three numbers is
`2 * 3 = 6`

So:

`6tu (5t + 2u + 4)`

Answer:

Option C

Question 2:

For this case we have that by definition of power properties of the same base, that:

`a ^ n * a ^ m = a ^ {n + m}`

That is, for multiplication of powers of the same base, the same base is placed and the exponents are added.

So:

`b ^ n * b ^ m = b ^ {n + m}`

ANswer:

`b ^ {n + m}`

Option A