Factor a^2-d^2+n^2-c^2-2an-2cd

Math
a2-d2+n2-c2-2an-2cd
Regroup terms.
a2+n2-2an-d2-c2-2cd
Factor using the perfect square rule.
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Rearrange terms.
a2-2an+n2-d2-c2-2cd
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
2an=2⋅a⋅n
Rewrite the polynomial.
a2-2⋅a⋅n+n2-d2-c2-2cd
Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=a and b=n.
(a-n)2-d2-c2-2cd
(a-n)2-d2-c2-2cd
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=-1⋅-1=1 and whose sum is b=-2.
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Reorder terms.
(a-n)2-c2-d2-2cd
Reorder -d2 and -2cd.
(a-n)2-c2-2cd-d2
Factor -2 out of -2cd.
(a-n)2-c2-2(cd)-d2
Rewrite -2 as -1 plus -1
(a-n)2-c2+(-1-1)(cd)-d2
Apply the distributive property.
(a-n)2-c2-1(cd)-1(cd)-d2
Remove unnecessary parentheses.
(a-n)2-c2-1cd-1(cd)-d2
Remove unnecessary parentheses.
(a-n)2-c2-1cd-1cd-d2
(a-n)2-c2-1cd-1cd-d2
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(a-n)2+(-c2-1cd)-1cd-d2
Factor out the greatest common factor (GCF) from each group.
(a-n)2+c(-c-1d)+d(-1c-d)
(a-n)2+c(-c-1d)+d(-1c-d)
Factor the polynomial by factoring out the greatest common factor, -c-1d.
(a-n)2+(-c-1d)(c+d)
(a-n)2+(-c-1d)(c+d)
Rewrite -1d as -d.
(a-n)2+(-c-d)(c+d)
Rewrite (c+d)(c+d) as (c+d)2.
(a-n)2-(c+d)2
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=a-n and b=c+d.
(a-n+c+d)(a-n-(c+d))
Apply the distributive property.
(a-n+c+d)(a-n-c-d)
Factor a^2-d^2+n^2-c^2-2an-2cd

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