Question

Need help in these to math problems

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