Algebra Examples

${(x^{2} - 6 x)}^{2} + (x^{2} - 6 x) - 56$

Step 1

The polynomial cannot be factored using the grouping method. Try a different method, or if you aren't sure, choose Factor.

The polynomial cannot be factored using the grouping method.

Step 2

Rewrite ${(x^{2} - 6 x)}^{2}$ as $(x^{2} - 6 x) (x^{2} - 6 x)$ .

$(x^{2} - 6 x) (x^{2} - 6 x) + x^{2} - 6 x - 56$

Step 3

Expand $(x^{2} - 6 x) (x^{2} - 6 x)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$x^{2} (x^{2} - 6 x) - 6 x (x^{2} - 6 x) + x^{2} - 6 x - 56$

Step 3.2

Apply the distributive property.

$x^{2} x^{2} + x^{2} (- 6 x) - 6 x (x^{2} - 6 x) + x^{2} - 6 x - 56$

Step 3.3

Apply the distributive property.

$x^{2} x^{2} + x^{2} (- 6 x) - 6 x \cdot x^{2} - 6 x (- 6 x) + x^{2} - 6 x - 56$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

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

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Step 4.1.1.1

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

$x^{2 + 2} + x^{2} (- 6 x) - 6 x \cdot x^{2} - 6 x (- 6 x) + x^{2} - 6 x - 56$

Step 4.1.1.2

Add $2$ and $2$ .

$x^{4} + x^{2} (- 6 x) - 6 x \cdot x^{2} - 6 x (- 6 x) + x^{2} - 6 x - 56$

Step 4.1.2

Rewrite using the commutative property of multiplication.

$x^{4} - 6 x^{2} x - 6 x \cdot x^{2} - 6 x (- 6 x) + x^{2} - 6 x - 56$

Step 4.1.3

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

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Step 4.1.3.1

Move $x$ .

$x^{4} - 6 (x \cdot x^{2}) - 6 x \cdot x^{2} - 6 x (- 6 x) + x^{2} - 6 x - 56$

Step 4.1.3.2

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

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Step 4.1.3.2.1

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

$x^{4} - 6 (x^{1} x^{2}) - 6 x \cdot x^{2} - 6 x (- 6 x) + x^{2} - 6 x - 56$

Step 4.1.3.2.2

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

$x^{4} - 6 x^{1 + 2} - 6 x \cdot x^{2} - 6 x (- 6 x) + x^{2} - 6 x - 56$

Step 4.1.3.3

Add $1$ and $2$ .

$x^{4} - 6 x^{3} - 6 x \cdot x^{2} - 6 x (- 6 x) + x^{2} - 6 x - 56$

Step 4.1.4

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

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Step 4.1.4.1

Move $x^{2}$ .

$x^{4} - 6 x^{3} - 6 (x^{2} x) - 6 x (- 6 x) + x^{2} - 6 x - 56$

Step 4.1.4.2

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

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Step 4.1.4.2.1

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

$x^{4} - 6 x^{3} - 6 (x^{2} x^{1}) - 6 x (- 6 x) + x^{2} - 6 x - 56$

Step 4.1.4.2.2

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

$x^{4} - 6 x^{3} - 6 x^{2 + 1} - 6 x (- 6 x) + x^{2} - 6 x - 56$

Step 4.1.4.3

Add $2$ and $1$ .

$x^{4} - 6 x^{3} - 6 x^{3} - 6 x (- 6 x) + x^{2} - 6 x - 56$

Step 4.1.5

Rewrite using the commutative property of multiplication.

$x^{4} - 6 x^{3} - 6 x^{3} - 6 \cdot - 6 x \cdot x + x^{2} - 6 x - 56$

Step 4.1.6

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

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Step 4.1.6.1

Move $x$ .

$x^{4} - 6 x^{3} - 6 x^{3} - 6 \cdot - 6 (x \cdot x) + x^{2} - 6 x - 56$

Step 4.1.6.2

Multiply $x$ by $x$ .

$x^{4} - 6 x^{3} - 6 x^{3} - 6 \cdot - 6 x^{2} + x^{2} - 6 x - 56$

Step 4.1.7

Multiply $- 6$ by $- 6$ .

$x^{4} - 6 x^{3} - 6 x^{3} + 36 x^{2} + x^{2} - 6 x - 56$

Step 4.2

Subtract $6 x^{3}$ from $- 6 x^{3}$ .

$x^{4} - 12 x^{3} + 36 x^{2} + x^{2} - 6 x - 56$

Step 5

Add $36 x^{2}$ and $x^{2}$ .

$x^{4} - 12 x^{3} + 37 x^{2} - 6 x - 56$