Algebra Examples

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

Step 1

Simplify terms.

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Rewrite $i^{2}$ as $- 1$ .

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

Step 1.1.2

Multiply $2$ by $- 1$ .

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

Step 1.2

Rewrite ${(- 2 + 3 a - 5 n)}^{2}$ as $(- 2 + 3 a - 5 n) (- 2 + 3 a - 5 n)$ .

$(- 2 + 3 a - 5 n) (- 2 + 3 a - 5 n)$

Step 2

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

$- 2 \cdot - 2 - 2 (3 a) - 2 (- 5 n) + 3 a \cdot - 2 + 3 a (3 a) + 3 a (- 5 n) - 5 n \cdot - 2 - 5 n (3 a) - 5 n (- 5 n)$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply $- 2$ by $- 2$ .

$4 - 2 (3 a) - 2 (- 5 n) + 3 a \cdot - 2 + 3 a (3 a) + 3 a (- 5 n) - 5 n \cdot - 2 - 5 n (3 a) - 5 n (- 5 n)$

Step 3.1.2

Multiply $3$ by $- 2$ .

$4 - 6 a - 2 (- 5 n) + 3 a \cdot - 2 + 3 a (3 a) + 3 a (- 5 n) - 5 n \cdot - 2 - 5 n (3 a) - 5 n (- 5 n)$

Step 3.1.3

Multiply $- 5$ by $- 2$ .

$4 - 6 a + 10 n + 3 a \cdot - 2 + 3 a (3 a) + 3 a (- 5 n) - 5 n \cdot - 2 - 5 n (3 a) - 5 n (- 5 n)$

Step 3.1.4

Multiply $- 2$ by $3$ .

$4 - 6 a + 10 n - 6 a + 3 a (3 a) + 3 a (- 5 n) - 5 n \cdot - 2 - 5 n (3 a) - 5 n (- 5 n)$

Step 3.1.5

Rewrite using the commutative property of multiplication.

$4 - 6 a + 10 n - 6 a + 3 \cdot 3 a \cdot a + 3 a (- 5 n) - 5 n \cdot - 2 - 5 n (3 a) - 5 n (- 5 n)$

Step 3.1.6

Multiply $a$ by $a$ by adding the exponents.

Tap for more steps...

Step 3.1.6.1

Move $a$ .

$4 - 6 a + 10 n - 6 a + 3 \cdot 3 (a \cdot a) + 3 a (- 5 n) - 5 n \cdot - 2 - 5 n (3 a) - 5 n (- 5 n)$

Step 3.1.6.2

Multiply $a$ by $a$ .

$4 - 6 a + 10 n - 6 a + 3 \cdot 3 a^{2} + 3 a (- 5 n) - 5 n \cdot - 2 - 5 n (3 a) - 5 n (- 5 n)$

Step 3.1.7

Multiply $3$ by $3$ .

$4 - 6 a + 10 n - 6 a + 9 a^{2} + 3 a (- 5 n) - 5 n \cdot - 2 - 5 n (3 a) - 5 n (- 5 n)$

Step 3.1.8

Rewrite using the commutative property of multiplication.

$4 - 6 a + 10 n - 6 a + 9 a^{2} + 3 \cdot - 5 a n - 5 n \cdot - 2 - 5 n (3 a) - 5 n (- 5 n)$

Step 3.1.9

Multiply $3$ by $- 5$ .

$4 - 6 a + 10 n - 6 a + 9 a^{2} - 15 a n - 5 n \cdot - 2 - 5 n (3 a) - 5 n (- 5 n)$

Step 3.1.10

Multiply $- 2$ by $- 5$ .

$4 - 6 a + 10 n - 6 a + 9 a^{2} - 15 a n + 10 n - 5 n (3 a) - 5 n (- 5 n)$

Step 3.1.11

Rewrite using the commutative property of multiplication.

$4 - 6 a + 10 n - 6 a + 9 a^{2} - 15 a n + 10 n - 5 \cdot 3 n a - 5 n (- 5 n)$

Step 3.1.12

Multiply $- 5$ by $3$ .

$4 - 6 a + 10 n - 6 a + 9 a^{2} - 15 a n + 10 n - 15 n a - 5 n (- 5 n)$

Step 3.1.13

Rewrite using the commutative property of multiplication.

$4 - 6 a + 10 n - 6 a + 9 a^{2} - 15 a n + 10 n - 15 n a - 5 \cdot - 5 n \cdot n$

Step 3.1.14

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

Tap for more steps...

Step 3.1.14.1

Move $n$ .

$4 - 6 a + 10 n - 6 a + 9 a^{2} - 15 a n + 10 n - 15 n a - 5 \cdot - 5 (n \cdot n)$

Step 3.1.14.2

Multiply $n$ by $n$ .

$4 - 6 a + 10 n - 6 a + 9 a^{2} - 15 a n + 10 n - 15 n a - 5 \cdot - 5 n^{2}$

Step 3.1.15

Multiply $- 5$ by $- 5$ .

$4 - 6 a + 10 n - 6 a + 9 a^{2} - 15 a n + 10 n - 15 n a + 25 n^{2}$

Step 3.2

Simplify by adding terms.

Tap for more steps...

Step 3.2.1

Subtract $6 a$ from $- 6 a$ .

$4 - 12 a + 10 n + 9 a^{2} - 15 a n + 10 n - 15 n a + 25 n^{2}$

Step 3.2.2

Add $10 n$ and $10 n$ .

$4 - 12 a + 9 a^{2} - 15 a n + 20 n - 15 n a + 25 n^{2}$

Step 4

Subtract $15 n a$ from $- 15 a n$ .

Tap for more steps...

Step 4.1

Move $n$ .

$4 - 12 a + 9 a^{2} - 15 a n - 15 a n + 20 n + 25 n^{2}$

Step 4.2

Subtract $15 a n$ from $- 15 a n$ .

$4 - 12 a + 9 a^{2} - 30 a n + 20 n + 25 n^{2}$