Algebra Examples

${(x + 4)}^{2} - 4 y^{5} (x + 4) + 4 y^{10}$

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

Factor by grouping.

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Step 2.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 4 \cdot 1 = 4$ and whose sum is $b = - 4$ .

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Step 2.1.1

Reorder terms.

$4 y^{10} + {(x + 4)}^{2} - 4 y^{5} (x + 4)$

Step 2.1.2

Reorder ${(x + 4)}^{2}$ and $- 4 y^{5} (x + 4)$ .

$4 y^{10} - 4 y^{5} (x + 4) + {(x + 4)}^{2}$

Step 2.1.3

Factor $- 4$ out of $- 4 y^{5} (x + 4)$ .

$4 y^{10} - 4 (y^{5} (x + 4)) + {(x + 4)}^{2}$

Step 2.1.4

Rewrite $- 4$ as $- 2$ plus $- 2$

$4 y^{10} + (- 2 - 2) (y^{5} (x + 4)) + {(x + 4)}^{2}$

Step 2.1.5

Apply the distributive property.

$4 y^{10} - 2 (y^{5} (x + 4)) - 2 (y^{5} (x + 4)) + {(x + 4)}^{2}$

Step 2.1.6

Remove unnecessary parentheses.

$4 y^{10} - 2 y^{5} (x + 4) - 2 (y^{5} (x + 4)) + {(x + 4)}^{2}$

Step 2.1.7

Remove unnecessary parentheses.

$4 y^{10} - 2 y^{5} (x + 4) - 2 y^{5} (x + 4) + {(x + 4)}^{2}$

Step 2.2

Factor out the greatest common factor from each group.

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Step 2.2.1

Group the first two terms and the last two terms.

$(4 y^{10} - 2 y^{5} (x + 4)) - 2 y^{5} (x + 4) + {(x + 4)}^{2}$

Step 2.2.2

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

$2 y^{5} (2 y^{5} - 1 (x + 4)) - (x + 4) (2 y^{5} - (x + 4))$

Step 2.3

Factor the polynomial by factoring out the greatest common factor, $2 y^{5} - 1 (x + 4)$ .

$(2 y^{5} - 1 (x + 4)) (2 y^{5} - (x + 4))$

Step 3

Apply the distributive property.

$(2 y^{5} - 1 x - 1 \cdot 4) (2 y^{5} - (x + 4))$

Step 4

Rewrite $- 1 x$ as $- x$ .

$(2 y^{5} - x - 1 \cdot 4) (2 y^{5} - (x + 4))$

Step 5

Multiply $- 1$ by $4$ .

$(2 y^{5} - x - 4) (2 y^{5} - (x + 4))$

Step 6

Apply the distributive property.

$(2 y^{5} - x - 4) (2 y^{5} - x - 1 \cdot 4)$

Step 7

Multiply $- 1$ by $4$ .

$(2 y^{5} - x - 4) (2 y^{5} - x - 4)$