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(x+5)(3xsquared-2x+1)

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(Remember PEMDAS! http://www.mathsisfun.com/operation-order-pemdas.html )

use the distributive property and solve

To expand the expression (x+5)(3x^2 - 2x + 1), we can use the distributive property. This means that we'll multiply each term in the first parentheses by each term in the second parentheses.

Step 1: Multiply the first term of the first parentheses (x) by each term in the second parentheses:
x * (3x^2 - 2x + 1) = 3x^3 - 2x^2 + x

Step 2: Multiply the second term of the first parentheses (+5) by each term in the second parentheses:
5 * (3x^2 - 2x + 1) = 15x^2 - 10x + 5

Step 3: Combine the results from step 1 and step 2 to get the fully expanded expression:
(x+5)(3x^2 - 2x + 1) = 3x^3 - 2x^2 + x + 15x^2 - 10x + 5

Simplifying the expression further, we can combine like terms:
3x^3 + (15x^2 - 2x^2) + (x - 10x) + 5
3x^3 + 13x^2 - 9x + 5

Therefore, (x+5)(3x^2 - 2x + 1) expands to 3x^3 + 13x^2 - 9x + 5.