Multiply (3a+5a^2b)(3a-5a^2b)

Math
(3a+5a2b)(3a-5a2b)
Expand (3a+5a2b)(3a-5a2b) using the FOIL Method.
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Apply the distributive property.
3a(3a-5a2b)+5a2b(3a-5a2b)
Apply the distributive property.
3a(3a)+3a(-5a2b)+5a2b(3a-5a2b)
Apply the distributive property.
3a(3a)+3a(-5a2b)+5a2b(3a)+5a2b(-5a2b)
3a(3a)+3a(-5a2b)+5a2b(3a)+5a2b(-5a2b)
Simplify and combine like terms.
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Simplify each term.
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Multiply a by a.
3⋅3a2+3a(-5a2b)+5a2b(3a)+5a2b(-5a2b)
Multiply 3 by 3.
9a2+3a(-5a2b)+5a2b(3a)+5a2b(-5a2b)
Multiply a by a2 by adding the exponents.
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Move a2.
9a2+3(a2a)(-5b)+5a2b(3a)+5a2b(-5a2b)
Multiply a2 by a.
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Raise a to the power of 1.
9a2+3(a2a1)(-5b)+5a2b(3a)+5a2b(-5a2b)
Use the power rule aman=am+n to combine exponents.
9a2+3a2+1(-5b)+5a2b(3a)+5a2b(-5a2b)
9a2+3a2+1(-5b)+5a2b(3a)+5a2b(-5a2b)
Add 2 and 1.
9a2+3a3(-5b)+5a2b(3a)+5a2b(-5a2b)
9a2+3a3(-5b)+5a2b(3a)+5a2b(-5a2b)
Rewrite using the commutative property of multiplication.
9a2+3⋅-5(a3b)+5a2b(3a)+5a2b(-5a2b)
Multiply 3 by -5.
9a2-15(a3b)+5a2b(3a)+5a2b(-5a2b)
Multiply a2 by a by adding the exponents.
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Move a.
9a2-15a3b+5(a⋅a2)b⋅3+5a2b(-5a2b)
Multiply a by a2.
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Raise a to the power of 1.
9a2-15a3b+5(a1a2)b⋅3+5a2b(-5a2b)
Use the power rule aman=am+n to combine exponents.
9a2-15a3b+5a1+2b⋅3+5a2b(-5a2b)
9a2-15a3b+5a1+2b⋅3+5a2b(-5a2b)
Add 1 and 2.
9a2-15a3b+5a3b⋅3+5a2b(-5a2b)
9a2-15a3b+5a3b⋅3+5a2b(-5a2b)
Multiply 3 by 5.
9a2-15a3b+15a3b+5a2b(-5a2b)
Multiply a2 by a2 by adding the exponents.
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Move a2.
9a2-15a3b+15a3b+5(a2a2)b(-5b)
Use the power rule aman=am+n to combine exponents.
9a2-15a3b+15a3b+5a2+2b(-5b)
Add 2 and 2.
9a2-15a3b+15a3b+5a4b(-5b)
9a2-15a3b+15a3b+5a4b(-5b)
Multiply b by b by adding the exponents.
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Move b.
9a2-15a3b+15a3b+5a4(b⋅b)⋅-5
Multiply b by b.
9a2-15a3b+15a3b+5a4b2⋅-5
9a2-15a3b+15a3b+5a4b2⋅-5
Multiply -5 by 5.
9a2-15a3b+15a3b-25a4b2
9a2-15a3b+15a3b-25a4b2
Add -15a3b and 15a3b.
9a2+0-25a4b2
Add 9a2 and 0.
9a2-25a4b2
9a2-25a4b2
Multiply (3a+5a^2b)(3a-5a^2b)

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