Write in Standard Form (2n^2-7n+2)(3n+1)

$(2 n^{2} - 7 n + 2) (3 n + 1)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Expand $(2 n^{2} - 7 n + 2) (3 n + 1)$ by multiplying each term in the first expression by each term in the second expression.

$2 n^{2} (3 n) + 2 n^{2} \cdot 1 - 7 n (3 n) - 7 n \cdot 1 + 2 (3 n) + 2 \cdot 1$

Step 3

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 3 n^{2} n + 2 n^{2} \cdot 1 - 7 n (3 n) - 7 n \cdot 1 + 2 (3 n) + 2 \cdot 1$

Multiply $n^{2}$ by $n$ by adding the exponents.

Move $n$ .

$2 \cdot 3 (n \cdot n^{2}) + 2 n^{2} \cdot 1 - 7 n (3 n) - 7 n \cdot 1 + 2 (3 n) + 2 \cdot 1$

Multiply $n$ by $n^{2}$ .

Raise $n$ to the power of $1$ .

$2 \cdot 3 (n^{1} n^{2}) + 2 n^{2} \cdot 1 - 7 n (3 n) - 7 n \cdot 1 + 2 (3 n) + 2 \cdot 1$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \cdot 3 n^{1 + 2} + 2 n^{2} \cdot 1 - 7 n (3 n) - 7 n \cdot 1 + 2 (3 n) + 2 \cdot 1$

Add $1$ and $2$ .

$2 \cdot 3 n^{3} + 2 n^{2} \cdot 1 - 7 n (3 n) - 7 n \cdot 1 + 2 (3 n) + 2 \cdot 1$

Multiply $2$ by $3$ .

$6 n^{3} + 2 n^{2} \cdot 1 - 7 n (3 n) - 7 n \cdot 1 + 2 (3 n) + 2 \cdot 1$

Multiply $2$ by $1$ .

$6 n^{3} + 2 n^{2} - 7 n (3 n) - 7 n \cdot 1 + 2 (3 n) + 2 \cdot 1$

Rewrite using the commutative property of multiplication.

$6 n^{3} + 2 n^{2} - 7 \cdot 3 n \cdot n - 7 n \cdot 1 + 2 (3 n) + 2 \cdot 1$

Multiply $n$ by $n$ by adding the exponents.

Move $n$ .

$6 n^{3} + 2 n^{2} - 7 \cdot 3 (n \cdot n) - 7 n \cdot 1 + 2 (3 n) + 2 \cdot 1$

Multiply $n$ by $n$ .

$6 n^{3} + 2 n^{2} - 7 \cdot 3 n^{2} - 7 n \cdot 1 + 2 (3 n) + 2 \cdot 1$

Multiply $- 7$ by $3$ .

$6 n^{3} + 2 n^{2} - 21 n^{2} - 7 n \cdot 1 + 2 (3 n) + 2 \cdot 1$

Multiply $- 7$ by $1$ .

$6 n^{3} + 2 n^{2} - 21 n^{2} - 7 n + 2 (3 n) + 2 \cdot 1$

Multiply $3$ by $2$ .

$6 n^{3} + 2 n^{2} - 21 n^{2} - 7 n + 6 n + 2 \cdot 1$

Multiply $2$ by $1$ .

$6 n^{3} + 2 n^{2} - 21 n^{2} - 7 n + 6 n + 2$

Simplify by adding terms.

Subtract $21 n^{2}$ from $2 n^{2}$ .

$6 n^{3} - 19 n^{2} - 7 n + 6 n + 2$

Add $- 7 n$ and $6 n$ .

$6 n^{3} - 19 n^{2} - n + 2$

Write in Standard Form (2n^2-7n+2)(3n+1)

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