Find the prime factorization of 2^5 · 3^3 · 5^37 + 8^2 · 3^4 · 5^35

Answer 1

1 Let's review a concept called, "Distributive Property".

3 sets of 2 plus 4 is equal to 3 sets of 2 plus 3 sets of 4 => 3(2+4) = 3x2 + 3x4 .

Alternatively, it can be written as ab+ac=a(b+c) where a is the greatest common factor.

For this question, you need to find the greatest common factors (the largest factors that both numbers are divisible by) and use the GCF like doing the distributive property backward.

2 What does 2⁵ means? Exponents of a number mean how many times to use the number in a multiplication. 2⁵ means 2 times itself for 5 times (2x2x2x2x2)

Therefore the greatest common factor of these 2 terms, 2⁵3³5³⁷ + 2⁶3⁴5³⁵ is 2⁵3³5³⁵ (2 times itself 5 times, 3 times itself 4 times, and 5 times itself 35 times).

Now use the GCF like doing the distributive property backward.

2⁵3³5³⁷ + 2⁶3⁴5³⁵ = 2⁵3³5³⁵(5² + 2*3*5²)

Answer 2

2⁵3³5³⁷ + 2⁶3⁴5³⁵

2⁵3³5³⁵(5² + 2*3*5²)