Algebra Examples

$P (x) = x^{2} (b^{2} x + a^{2}) + a b (x^{5} + 1)$

Step 1

Write $P (x) = x^{2} (b^{2} x + a^{2}) + a b (x^{5} + 1)$ as an equation.

$y = x^{2} (b^{2} x + a^{2}) + a b (x^{5} + 1)$

Step 2

Simplify $x^{2} (b^{2} x + a^{2}) + a b (x^{5} + 1)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$y = x^{2} (b^{2} x) + x^{2} a^{2} + a b (x^{5} + 1)$

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

$y = x \cdot x^{2} b^{2} + x^{2} a^{2} + a b (x^{5} + 1)$

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 $1$ .

$y = x^{1} x^{2} b^{2} + x^{2} a^{2} + a b (x^{5} + 1)$

Step 2.1.2.2.2

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

$y = x^{1 + 2} b^{2} + x^{2} a^{2} + a b (x^{5} + 1)$

Step 2.1.2.3

Add $1$ and $2$ .

$y = x^{3} b^{2} + x^{2} a^{2} + a b (x^{5} + 1)$

Step 2.1.3

Apply the distributive property.

$y = x^{3} b^{2} + x^{2} a^{2} + a b x^{5} + a b \cdot 1$

Step 2.1.4

Multiply $a$ by $1$ .

$y = x^{3} b^{2} + x^{2} a^{2} + a b x^{5} + a b$

Step 2.2

Simplify the expression.

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Step 2.2.1

Reorder $x^{3}$ and $b^{2}$ .

$y = b^{2} x^{3} + x^{2} a^{2} + a b x^{5} + a b$

Step 2.2.2

Reorder $x^{2}$ and $a^{2}$ .

$y = b^{2} x^{3} + a^{2} x^{2} + a b x^{5} + a b$

Step 2.2.3

Move $a^{2} x^{2}$ .

$y = b^{2} x^{3} + a b x^{5} + a^{2} x^{2} + a b$

Step 2.2.4

Reorder $b^{2} x^{3}$ and $a b x^{5}$ .

$y = a b x^{5} + b^{2} x^{3} + a^{2} x^{2} + a b$