how do you factor problems like (w^3)(x^2)-(10w^3)(x)+25w^3?

(w^3)(x^2)-(10w^3)(x)+25w^3?

first factor out w^3
w^3 [ x^2 -10x +25 ]
w^3 (x-5)(x-5)

To factor the expression (w^3)(x^2) - (10w^3)(x) + 25w^3, we can notice that there is a common factor of w^3 in each term. We can factor it out by factoring w^3 from each term individually.

Step 1: Factor out the common factor w^3:

(w^3)(x^2) - (10w^3)(x) + 25w^3
= w^3(x^2 - 10x + 25)

Now, we have simplified the expression by factoring out the common factor w^3.

Step 2: Simplify the expression inside the parentheses, which is now (x^2 - 10x + 25).

To further factorize the expression inside the parentheses, we can look for factors that multiply to the constant term (25) and add up to the coefficient of the linear term (-10).

In this case, the factors of 25 are 1 and 25, and their sum is 26 (1 + 25 = 26). Since these factors add up to -10, they can be used to factorize the expression.

Step 3: Factorize the expression (x^2 - 10x + 25):

(x^2 - 10x + 25) can be factored as (x - 5)(x - 5) or (x - 5)^2

Finally, we can rewrite the factored expression with the simplified expression inside the parentheses:

(w^3)(x^2) - (10w^3)(x) + 25w^3 = w^3(x - 5)^2

Therefore, the fully factored form of the given expression is w^3(x - 5)^2.