Pre-Algebra Examples

$P (x) = x^{4} - 2 x^{3} - 3 x^{2} \cdot (8 x) - 4$

Step 1

Rewrite the function as an equation.

$y = x^{4} - 2 x^{3} - 3 x^{2} \cdot (8 x) - 4$

Step 2

Simplify $x^{4} - 2 x^{3} - 3 x^{2} \cdot (8 x) - 4$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$y = x^{4} - 2 x^{3} - 3 \cdot 8 x^{2} x - 4$

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

$y = x^{4} - 2 x^{3} - 3 \cdot 8 (x \cdot x^{2}) - 4$

Step 2.1.2.2

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

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Step 2.1.2.2.1

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

$y = x^{4} - 2 x^{3} - 3 \cdot 8 (x^{1} x^{2}) - 4$

Step 2.1.2.2.2

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

$y = x^{4} - 2 x^{3} - 3 \cdot 8 x^{1 + 2} - 4$

Step 2.1.2.3

Add $1$ and $2$ .

$y = x^{4} - 2 x^{3} - 3 \cdot 8 x^{3} - 4$

Step 2.1.3

Multiply $- 3$ by $8$ .

$y = x^{4} - 2 x^{3} - 24 x^{3} - 4$

Step 2.2

Subtract $24 x^{3}$ from $- 2 x^{3}$ .

$y = x^{4} - 26 x^{3} - 4$