Precalculus Examples

${(8 + 9 j)}^{2}$

Step 1

Rewrite ${(8 + 9 j)}^{2}$ as $(8 + 9 j) (8 + 9 j)$ .

$(8 + 9 j) (8 + 9 j)$

Step 2

Expand $(8 + 9 j) (8 + 9 j)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$8 (8 + 9 j) + 9 j (8 + 9 j)$

Step 2.2

Apply the distributive property.

$8 \cdot 8 + 8 (9 j) + 9 j (8 + 9 j)$

Step 2.3

Apply the distributive property.

$8 \cdot 8 + 8 (9 j) + 9 j \cdot 8 + 9 j (9 j)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $8$ by $8$ .

$64 + 8 (9 j) + 9 j \cdot 8 + 9 j (9 j)$

Step 3.1.2

Multiply $9$ by $8$ .

$64 + 72 j + 9 j \cdot 8 + 9 j (9 j)$

Step 3.1.3

Multiply $8$ by $9$ .

$64 + 72 j + 72 j + 9 j (9 j)$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$64 + 72 j + 72 j + 9 \cdot 9 j \cdot j$

Step 3.1.5

Multiply $j$ by $j$ by adding the exponents.

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Step 3.1.5.1

Move $j$ .

$64 + 72 j + 72 j + 9 \cdot 9 (j \cdot j)$

Step 3.1.5.2

Multiply $j$ by $j$ .

$64 + 72 j + 72 j + 9 \cdot 9 j^{2}$

Step 3.1.6

Multiply $9$ by $9$ .

$64 + 72 j + 72 j + 81 j^{2}$

Step 3.2

Add $72 j$ and $72 j$ .

$64 + 144 j + 81 j^{2}$