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Algebraic Structures 1
Contributed by: Heseltine
1-4x2=
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(1-4x)2
(1-2x)(1+2x)
(1-2x)2
X4-Y2=
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(X4+Y)(X4-Y)
(X+Y)(X-Y)
(X2+Y)(X2-Y)
(1-x)2=
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1-2x-x2
1-2x-2x2
1-2x+x2
(p+3q)2=
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p2+3pq+9q2
p2+9pq+6q2
p2+6pq+9q2
(2p+3q)2=
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4p2+12pq+9q2
2p2+6pq+9q2
4p2+6pq+9q2
(2p-3q)2=
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4p2+12pq-9q2
p2-6pq+9q2
4p2-12pq+9q2
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(p2-2)2=
p4+4p2-4
4p2-4p+4
p4-4p2+4
(p2-2)(p2+2)=
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p4-4
4p2-4
p4-4p2+4
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(p2-4)2=
p4+8p2-16
(p-2)2(p+2)2
p4-8p2+16
(pq2-p2q)2=
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(pq2)2-2p3q3+(p2q)2
p2q4-2p3q3+p4q2
p2q4+2p3q3-p4q2
(pq2-p2q)(pq2+p2q)=
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(pq2)2-(p2q)2
p2q4-p4q2
p2q4+p4q2
(p6-4)(p6+4)=
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(p3-2)(p3+2)(p6+4)
p12-16
(p3-2)(p3+2)3
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