Algebra Examples

$x^{2} - 8 x + 3$ , $x = 4 + i$

Step 1

Replace the variable $x$ with $4 + i$ in the expression.

${(4 + i)}^{2} - 8 (4 + i) + 3$

Step 2

Simplify each term.

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Step 2.1

Rewrite ${(4 + i)}^{2}$ as $(4 + i) (4 + i)$ .

$(4 + i) (4 + i) - 8 (4 + i) + 3$

Step 2.2

Expand $(4 + i) (4 + i)$ using the FOIL Method.

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Step 2.2.1

Apply the distributive property.

$4 (4 + i) + i (4 + i) - 8 (4 + i) + 3$

Step 2.2.2

Apply the distributive property.

$4 \cdot 4 + 4 i + i (4 + i) - 8 (4 + i) + 3$

Step 2.2.3

Apply the distributive property.

$4 \cdot 4 + 4 i + i \cdot 4 + i i - 8 (4 + i) + 3$

Step 2.3

Simplify and combine like terms.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Multiply $4$ by $4$ .

$16 + 4 i + i \cdot 4 + i i - 8 (4 + i) + 3$

Step 2.3.1.2

Move $4$ to the left of $i$ .

$16 + 4 i + 4 \cdot i + i i - 8 (4 + i) + 3$

Step 2.3.1.3

Multiply $i i$ .

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Step 2.3.1.3.1

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

$16 + 4 i + 4 i + i^{1} i - 8 (4 + i) + 3$

Step 2.3.1.3.2

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

$16 + 4 i + 4 i + i^{1} i^{1} - 8 (4 + i) + 3$

Step 2.3.1.3.3

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

$16 + 4 i + 4 i + i^{1 + 1} - 8 (4 + i) + 3$

Step 2.3.1.3.4

Add $1$ and $1$ .

$16 + 4 i + 4 i + i^{2} - 8 (4 + i) + 3$

Step 2.3.1.4

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

$16 + 4 i + 4 i - 1 - 8 (4 + i) + 3$

Step 2.3.2

Subtract $1$ from $16$ .

$15 + 4 i + 4 i - 8 (4 + i) + 3$

Step 2.3.3

Add $4 i$ and $4 i$ .

$15 + 8 i - 8 (4 + i) + 3$

Step 2.4

Apply the distributive property.

$15 + 8 i - 8 \cdot 4 - 8 i + 3$

Step 2.5

Multiply $- 8$ by $4$ .

$15 + 8 i - 32 - 8 i + 3$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $32$ from $15$ .

$- 17 + 8 i - 8 i + 3$

Step 3.2

Add $- 17$ and $3$ .

$- 14 + 8 i - 8 i$

Step 3.3

Subtract $8 i$ from $8 i$ .

$- 14 + 0$

Step 3.4

Add $- 14$ and $0$ .

$- 14$