multiply. give your answer in standard form. (2n^2-7n+2)*(3n+1)
I'll get you started...
(2n^2-7n+2)*(3n+1)
= (2n^2-7n+2)*3n + (2n^2-7n+2)*1
Now just expand each factor term by term, simplifying at the end.
(2n^2-7n+2)*(3n+1)
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Here are the steps to multiply this expression using the distributive property:
1. Multiply the first term of the first expression (2n^2) by each term in the second expression (3n and 1), and write the products down:
2n^2 * 3n = 6n^3
2n^2 * 1 = 2n^2
2. Multiply the second term of the first expression (-7n) by each term in the second expression (3n and 1), and write the products down:
-7n * 3n = -21n^2
-7n * 1 = -7n
3. Multiply the third term of the first expression (2) by each term in the second expression (3n and 1), and write the products down:
2 * 3n = 6n
2 * 1 = 2
4. Add up all of the products from steps 1-3:
6n^3 - 21n^2 + 6n + 2n^2 - 7n + 2
5. Simplify the expression by combining like terms:
6n^3 - 19n^2 - n + 2
Therefore, the product of (2n^2-7n+2) and (3n+1) is 6n^3 - 19n^2 - n + 2.
To multiply the given expression (2n^2 - 7n + 2) * (3n + 1) and obtain the answer in standard form, we need to apply the distributive property and then combine like terms.
Let's go step by step:
Step 1: Multiply the first term in the first parentheses (2n^2) by each term in the second parentheses (3n + 1).
2n^2 * 3n = 6n^3
2n^2 * 1 = 2n^2
Step 2: Multiply the second term in the first parentheses (-7n) by each term in the second parentheses (3n + 1).
-7n * 3n = -21n^2
-7n * 1 = -7n
Step 3: Multiply the last term in the first parentheses (2) by each term in the second parentheses (3n + 1).
2 * 3n = 6n
2 * 1 = 2
Step 4: Now, we combine the like terms obtained in steps 1, 2, and 3.
Combining the n^3 terms: 6n^3 + 0n^2 (there are no other terms with n^3).
Combining the n^2 terms: 0n^3 - 21n^2 + 2n^2 = -19n^2
Combining the n terms: 0n^3 - 7n + 6n = -n
Combining the constant terms: 0n^3 + 0n^2 + 2 + 0 = 2
Putting all the terms together, we have:
6n^3 - 19n^2 - n + 2
This is the answer in standard form after multiplying the given expression.