Please Answer this and show your work!

(3h+2)(2h^2-7h+1)

Use the distributive property of multiplication

3h (2h^2-7h+1)
+
2 (2h^2-7h+1)

then collect like terms

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3h + (-7h)

To expand the given expression (3h+2)(2h^2-7h+1), we can use the distributive property of multiplication. This property states that when we multiply a value by a sum or difference of two or more terms, we distribute the value to each term individually.

To expand the expression, we multiply each term of the first factor by each term of the second factor and then combine like terms.

Let's break it down step by step:

Step 1: Multiply the first term of the first factor (3h) by each term of the second factor:
3h * 2h^2 = 6h^3
3h * -7h = -21h^2
3h * 1 = 3h

Step 2: Multiply the second term of the first factor (2) by each term of the second factor:
2 * 2h^2 = 4h^2
2 * -7h = -14h
2 * 1 = 2

Step 3: Combine like terms:
(6h^3) + (-21h^2) + (3h) + (4h^2) + (-14h) + (2)

Simplifying further by combining like terms gives us the final answer:

6h^3 - 17h^2 - 11h + 2

Therefore, the expansion of the given expression is 6h^3 - 17h^2 - 11h + 2.