Simplify ((3m-5n)+p)((3m-5n)-p)

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((3m-5n)+p)((3m-5n)-p)
Expand (3m-5n+p)(3m-5n-p) by multiplying each term in the first expression by each term in the second expression.
3m(3m)+3m(-5n)+3m(-p)-5n(3m)-5n(-5n)-5n(-p)+p(3m)+p(-5n)+p(-p)
Simplify terms.
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Simplify each term.
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Multiply m by m.
3⋅3m2+3m(-5n)+3m(-p)-5n(3m)-5n(-5n)-5n(-p)+p(3m)+p(-5n)+p(-p)
Multiply 3 by 3.
9m2+3m(-5n)+3m(-p)-5n(3m)-5n(-5n)-5n(-p)+p(3m)+p(-5n)+p(-p)
Rewrite using the commutative property of multiplication.
9m2+3⋅-5(mn)+3m(-p)-5n(3m)-5n(-5n)-5n(-p)+p(3m)+p(-5n)+p(-p)
Multiply 3 by -5.
9m2-15(mn)+3m(-p)-5n(3m)-5n(-5n)-5n(-p)+p(3m)+p(-5n)+p(-p)
Rewrite using the commutative property of multiplication.
9m2-15mn+3⋅-1(mp)-5n(3m)-5n(-5n)-5n(-p)+p(3m)+p(-5n)+p(-p)
Multiply 3 by -1.
9m2-15mn-3(mp)-5n(3m)-5n(-5n)-5n(-p)+p(3m)+p(-5n)+p(-p)
Rewrite using the commutative property of multiplication.
9m2-15mn-3mp-5⋅3(nm)-5n(-5n)-5n(-p)+p(3m)+p(-5n)+p(-p)
Multiply -5 by 3.
9m2-15mn-3mp-15(nm)-5n(-5n)-5n(-p)+p(3m)+p(-5n)+p(-p)
Multiply n by n.
9m2-15mn-3mp-15nm-5⋅-5n2-5n(-p)+p(3m)+p(-5n)+p(-p)
Multiply -5 by -5.
9m2-15mn-3mp-15nm+25n2-5n(-p)+p(3m)+p(-5n)+p(-p)
Rewrite using the commutative property of multiplication.
9m2-15mn-3mp-15nm+25n2-5⋅-1(np)+p(3m)+p(-5n)+p(-p)
Multiply -5 by -1.
9m2-15mn-3mp-15nm+25n2+5(np)+p(3m)+p(-5n)+p(-p)
Rewrite using the commutative property of multiplication.
9m2-15mn-3mp-15nm+25n2+5np+3pm+p(-5n)+p(-p)
Rewrite using the commutative property of multiplication.
9m2-15mn-3mp-15nm+25n2+5np+3pm-5pn+p(-p)
Rewrite using the commutative property of multiplication.
9m2-15mn-3mp-15nm+25n2+5np+3pm-5pn-p⋅p
Multiply p by p by adding the exponents.
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Move p.
9m2-15mn-3mp-15nm+25n2+5np+3pm-5pn-(p⋅p)
Multiply p by p.
9m2-15mn-3mp-15nm+25n2+5np+3pm-5pn-p2
9m2-15mn-3mp-15nm+25n2+5np+3pm-5pn-p2
9m2-15mn-3mp-15nm+25n2+5np+3pm-5pn-p2
Combine the opposite terms in 9m2-15mn-3mp-15nm+25n2+5np+3pm-5pn-p2.
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Reorder the factors in the terms -3mp and 3pm.
9m2-15mn-3mp-15nm+25n2+5np+3mp-5pn-p2
Add -3mp and 3mp.
9m2-15mn-15nm+25n2+5np+0-5pn-p2
Add 9m2-15mn-15nm+25n2+5np and 0.
9m2-15mn-15nm+25n2+5np-5pn-p2
Reorder the factors in the terms 5np and -5pn.
9m2-15mn-15nm+25n2+5np-5np-p2
Subtract 5np from 5np.
9m2-15mn-15nm+25n2+0-p2
Add 9m2-15mn-15nm+25n2 and 0.
9m2-15mn-15nm+25n2-p2
9m2-15mn-15nm+25n2-p2
9m2-15mn-15nm+25n2-p2
Subtract 15nm from -15mn.
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Move n.
9m2-15mn-15mn+25n2-p2
Subtract 15mn from -15mn.
9m2-30mn+25n2-p2
9m2-30mn+25n2-p2
Simplify ((3m-5n)+p)((3m-5n)-p)

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