Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

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

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Step 2.1

Move $a$ .

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

Step 2.2

Multiply $a$ by $a$ .

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

Step 3

Rewrite $x^{2} + b x - a^{2} - a b$ in a factored form.

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Step 3.1

Regroup terms.

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

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = a$ .

$(x + a) (x - a) + b x - a b$

Step 3.3

Factor $b$ out of $b x - a b$ .

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Step 3.3.1

Factor $b$ out of $b x$ .

$(x + a) (x - a) + b (x) - a b$

Step 3.3.2

Factor $b$ out of $- a b$ .

$(x + a) (x - a) + b (x) + b (- a)$

Step 3.3.3

Factor $b$ out of $b (x) + b (- a)$ .

$(x + a) (x - a) + b (x - a)$

Step 3.4

Factor $x - a$ out of $(x + a) (x - a) + b (x - a)$ .

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Step 3.4.1

Factor $x - a$ out of $(x + a) (x - a)$ .

$(x - a) (x + a) + b (x - a)$

Step 3.4.2

Factor $x - a$ out of $b (x - a)$ .

$(x - a) (x + a) + (x - a) b$

Step 3.4.3

Factor $x - a$ out of $(x - a) (x + a) + (x - a) b$ .

$(x - a) (x + a + b)$