Simplify (x-a)(x^2+ax+a^2)

$(x - a) (x^{2} + a x + a^{2})$

Step 1

Expand $(x - a) (x^{2} + a x + a^{2})$ by multiplying each term in the first expression by each term in the second expression.

$x \cdot x^{2} + x (a x) + x a^{2} - a x^{2} - a (a x) - a \cdot a^{2}$

Step 2

Simplify terms.

Simplify each term.

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

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

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

$x^{1} x^{2} + x (a x) + x a^{2} - a x^{2} - a (a x) - a \cdot a^{2}$

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

$x^{1 + 2} + x (a x) + x a^{2} - a x^{2} - a (a x) - a \cdot a^{2}$

Add $1$ and $2$ .

$x^{3} + x (a x) + x a^{2} - a x^{2} - a (a x) - a \cdot a^{2}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$x^{3} + x \cdot x a + x a^{2} - a x^{2} - a (a x) - a \cdot a^{2}$

Multiply $x$ by $x$ .

$x^{3} + x^{2} a + x a^{2} - a x^{2} - a (a x) - a \cdot a^{2}$

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

Move $a$ .

$x^{3} + x^{2} a + x a^{2} - a x^{2} - (a \cdot a) x - a \cdot a^{2}$

Multiply $a$ by $a$ .

$x^{3} + x^{2} a + x a^{2} - a x^{2} - a^{2} x - a \cdot a^{2}$

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

Move $a^{2}$ .

$x^{3} + x^{2} a + x a^{2} - a x^{2} - a^{2} x - (a^{2} a)$

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

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

$x^{3} + x^{2} a + x a^{2} - a x^{2} - a^{2} x - (a^{2} a^{1})$

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

$x^{3} + x^{2} a + x a^{2} - a x^{2} - a^{2} x - a^{2 + 1}$

Add $2$ and $1$ .

$x^{3} + x^{2} a + x a^{2} - a x^{2} - a^{2} x - a^{3}$

Combine the opposite terms in $x^{3} + x^{2} a + x a^{2} - a x^{2} - a^{2} x - a^{3}$ .

Reorder the factors in the terms $x^{2} a$ and $- a x^{2}$ .

$x^{3} + x^{2} a + x a^{2} - x^{2} a - a^{2} x - a^{3}$

Subtract $x^{2} a$ from $x^{2} a$ .

$x^{3} + x a^{2} + 0 - a^{2} x - a^{3}$

Add $x^{3} + x a^{2}$ and $0$ .

$x^{3} + x a^{2} - a^{2} x - a^{3}$

Reorder the factors in the terms $x a^{2}$ and $- a^{2} x$ .

$x^{3} + a^{2} x - a^{2} x - a^{3}$

Subtract $a^{2} x$ from $a^{2} x$ .

$x^{3} + 0 - a^{3}$

Add $x^{3}$ and $0$ .

$x^{3} - a^{3}$

Simplify (x-a)(x^2+ax+a^2)

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