3 times 5 equals 15
15 times 5 equals 75
75 times 5 equals 375
hope this helped (:
PART A. Notice that we have

as a common factor in all the terms, so lets factor that out:


Now we need can factor

:


We can conclude that the complete factorization of

is

.
PART 2. Here we just have a quadratic expression of the form

. To factor it, we are going to find <span>two numbers that will multiply to be equal the </span>c<span>, and will also add up to equal </span><span>b. Those numbers are 2 and 2:
</span>

Since both factors are equal, we can factor the expression even more:

We can conclude that the complete factorization of

is

.
PART C. Here we have a difference of squares. Notice that 4, can be written as

, so we can rewrite our expression:

Now we can factor our difference of squares like follows:

We can conclude that the complete factorization of

is
The general formula for the sides of right triangle is
a² + b² = c²
Subtitute the equation of a and b to the formula a² + b², evaluate if the answer will be the same as the equation of c²
a² + b²
= (m² - n²)² + (2mn)²
= (m² - n²)(m² - n²) + (2mn)(2mn)
= (m⁴ - 2m²n² + n⁴) + 4m²n²
= m⁴ + 2m²n² + n⁴
Factorize the result
m⁴ + 2m²n² + n⁴
= (m² + n²)(m² + n²)
= (m² + n²)²
= c²
It's proven by the formula that c² = (m² + n²)²
so the c will be m² + n²