Find the product.

x^3 (x2 + 5x + 1)

The product is;

x^5+5 x^4+x^3

Explanation:

Find the product;

x^3 (x2+5x+1)

Step 1: Open the bracket

To open the bracket, we need to multiple the term outsied the bracket (x^3) each of the terms inside the brackets; x2, 5x and 1

This can be done as follows;

(x3*x2) + (x3*5x) + (x3*1)

Step 2: Solve

Since the product of x3 and x2, have the same base x, it can be solved by maintaining the base x and getting the sum of the powers 3 and 2. This can be written as;

x^ (3+2) = x^5

To solve the product of 5 x and x^3, we use the same concept as above as shown;

(5 x) * (x^3), adding the powers of x and x^3 as shown;

5 x^ (1+3) = 5 x^4

In solving the product of x^3 and 1 the answer will just be x^3 since any term multiplied by 1 equals the same term.

In that case;

x^3

Step 3: Put the results of the terms together

(x^5) + 5 (x^4) + x^3

This can be further simplified to;

x^5+5 x^4+x^3