Algebra Examples

x^{3} + x^{2} = 4 x + 4

$x^{3} + x^{2} = 4 x + 4$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract

4 x

$4 x$ from both sides of the equation.

x^{3} + x^{2} - 4 x = 4

$x^{3} + x^{2} - 4 x = 4$

Step 1.2

Subtract

4

$4$ from both sides of the equation.

x^{3} + x^{2} - 4 x - 4 = 0

$x^{3} + x^{2} - 4 x - 4 = 0$

x^{3} + x^{2} - 4 x - 4 = 0

$x^{3} + x^{2} - 4 x - 4 = 0$

Step 2

Factor the left side.

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Step 2.1

Factor out the greatest common factor from each group.

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Step 2.1.1

Group the first two terms and the last two terms.

(x^{3} + x^{2}) - 4 x - 4 = 0

$(x^{3} + x^{2}) - 4 x - 4 = 0$

Step 2.1.2

Factor out the greatest common factor (GCF) from each group.

x^{2} (x + 1) - 4 (x + 1) = 0

$x^{2} (x + 1) - 4 (x + 1) = 0$

x^{2} (x + 1) - 4 (x + 1) = 0

$x^{2} (x + 1) - 4 (x + 1) = 0$

Step 2.2

Factor the polynomial by factoring out the greatest common factor,

x + 1

$x + 1$ .

(x + 1) (x^{2} - 4) = 0

$(x + 1) (x^{2} - 4) = 0$

Step 2.3

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

(x + 1) (x^{2} - 2^{2}) = 0

$(x + 1) (x^{2} - 2^{2}) = 0$

Step 2.4

Factor.

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Step 2.4.1

Since both terms are perfect squares, factor using the difference of squares formula,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ where

a = x

$a = x$ and

b = 2

$b = 2$ .

(x + 1) ((x + 2) (x - 2)) = 0

$(x + 1) ((x + 2) (x - 2)) = 0$

Step 2.4.2

Remove unnecessary parentheses.

(x + 1) (x + 2) (x - 2) = 0

$(x + 1) (x + 2) (x - 2) = 0$

(x + 1) (x + 2) (x - 2) = 0

$(x + 1) (x + 2) (x - 2) = 0$

(x + 1) (x + 2) (x - 2) = 0

$(x + 1) (x + 2) (x - 2) = 0$