Simplify (2n^2-3)(n^2+5n-1)

$(2 n^{2} - 3) (n^{2} + 5 n - 1)$

Step 1

Expand $(2 n^{2} - 3) (n^{2} + 5 n - 1)$ by multiplying each term in the first expression by each term in the second expression.

$2 n^{2} n^{2} + 2 n^{2} (5 n) + 2 n^{2} \cdot - 1 - 3 n^{2} - 3 (5 n) - 3 \cdot - 1$

Step 2

Simplify terms.

Simplify each term.

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

Move $n^{2}$ .

$2 (n^{2} n^{2}) + 2 n^{2} (5 n) + 2 n^{2} \cdot - 1 - 3 n^{2} - 3 (5 n) - 3 \cdot - 1$

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

$2 n^{2 + 2} + 2 n^{2} (5 n) + 2 n^{2} \cdot - 1 - 3 n^{2} - 3 (5 n) - 3 \cdot - 1$

Add $2$ and $2$ .

$2 n^{4} + 2 n^{2} (5 n) + 2 n^{2} \cdot - 1 - 3 n^{2} - 3 (5 n) - 3 \cdot - 1$

Rewrite using the commutative property of multiplication.

$2 n^{4} + 2 \cdot 5 n^{2} n + 2 n^{2} \cdot - 1 - 3 n^{2} - 3 (5 n) - 3 \cdot - 1$

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

Move $n$ .

$2 n^{4} + 2 \cdot 5 (n \cdot n^{2}) + 2 n^{2} \cdot - 1 - 3 n^{2} - 3 (5 n) - 3 \cdot - 1$

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

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

$2 n^{4} + 2 \cdot 5 (n^{1} n^{2}) + 2 n^{2} \cdot - 1 - 3 n^{2} - 3 (5 n) - 3 \cdot - 1$

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

$2 n^{4} + 2 \cdot 5 n^{1 + 2} + 2 n^{2} \cdot - 1 - 3 n^{2} - 3 (5 n) - 3 \cdot - 1$

Add $1$ and $2$ .

$2 n^{4} + 2 \cdot 5 n^{3} + 2 n^{2} \cdot - 1 - 3 n^{2} - 3 (5 n) - 3 \cdot - 1$

Multiply $2$ by $5$ .

$2 n^{4} + 10 n^{3} + 2 n^{2} \cdot - 1 - 3 n^{2} - 3 (5 n) - 3 \cdot - 1$

Multiply $- 1$ by $2$ .

$2 n^{4} + 10 n^{3} - 2 n^{2} - 3 n^{2} - 3 (5 n) - 3 \cdot - 1$

Multiply $5$ by $- 3$ .

$2 n^{4} + 10 n^{3} - 2 n^{2} - 3 n^{2} - 15 n - 3 \cdot - 1$

Multiply $- 3$ by $- 1$ .

$2 n^{4} + 10 n^{3} - 2 n^{2} - 3 n^{2} - 15 n + 3$

Subtract $3 n^{2}$ from $- 2 n^{2}$ .

$2 n^{4} + 10 n^{3} - 5 n^{2} - 15 n + 3$