Factor by Grouping (x^2+6x)^2+(x^2+6x)-56

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

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.

Apply the distributive property.

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

Apply the distributive property.

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

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.

Simplify each term.

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

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

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

Add $2$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $6$ by $6$ .

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

Add $6 x^{3}$ and $6 x^{3}$ .

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

Step 5

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

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

Factor by Grouping (x^2+6x)^2+(x^2+6x)-56

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