Simplify (-6w^2+9w-5)+(7w^2+9w-7)(9w^2+5w-2)

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(-6w2+9w-5)+(7w2+9w-7)(9w2+5w-2)
Simplify each term.
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Expand (7w2+9w-7)(9w2+5w-2) by multiplying each term in the first expression by each term in the second expression.
-6w2+9w-5+7w2(9w2)+7w2(5w)+7w2⋅-2+9w(9w2)+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
Simplify each term.
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Rewrite using the commutative property of multiplication.
-6w2+9w-5+7⋅9(w2w2)+7w2(5w)+7w2⋅-2+9w(9w2)+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
Multiply w2 by w2 by adding the exponents.
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Use the power rule aman=am+n to combine exponents.
-6w2+9w-5+7⋅9w2+2+7w2(5w)+7w2⋅-2+9w(9w2)+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
Add 2 and 2.
-6w2+9w-5+7⋅9w4+7w2(5w)+7w2⋅-2+9w(9w2)+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
-6w2+9w-5+7⋅9w4+7w2(5w)+7w2⋅-2+9w(9w2)+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
Multiply 7 by 9.
-6w2+9w-5+63w4+7w2(5w)+7w2⋅-2+9w(9w2)+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
Rewrite using the commutative property of multiplication.
-6w2+9w-5+63w4+7⋅5(w2w)+7w2⋅-2+9w(9w2)+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
Multiply w2 by w by adding the exponents.
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Multiply w2 by w.
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Raise w to the power of 1.
-6w2+9w-5+63w4+7⋅5(w2w1)+7w2⋅-2+9w(9w2)+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
Use the power rule aman=am+n to combine exponents.
-6w2+9w-5+63w4+7⋅5w2+1+7w2⋅-2+9w(9w2)+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
-6w2+9w-5+63w4+7⋅5w2+1+7w2⋅-2+9w(9w2)+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
Add 2 and 1.
-6w2+9w-5+63w4+7⋅5w3+7w2⋅-2+9w(9w2)+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
-6w2+9w-5+63w4+7⋅5w3+7w2⋅-2+9w(9w2)+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
Multiply 7 by 5.
-6w2+9w-5+63w4+35w3+7w2⋅-2+9w(9w2)+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
Multiply -2 by 7.
-6w2+9w-5+63w4+35w3-14w2+9w(9w2)+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
Rewrite using the commutative property of multiplication.
-6w2+9w-5+63w4+35w3-14w2+9⋅9(w⋅w2)+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
Multiply w by w2 by adding the exponents.
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Multiply w by w2.
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Raise w to the power of 1.
-6w2+9w-5+63w4+35w3-14w2+9⋅9(w1w2)+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
Use the power rule aman=am+n to combine exponents.
-6w2+9w-5+63w4+35w3-14w2+9⋅9w1+2+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
-6w2+9w-5+63w4+35w3-14w2+9⋅9w1+2+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
Add 1 and 2.
-6w2+9w-5+63w4+35w3-14w2+9⋅9w3+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
-6w2+9w-5+63w4+35w3-14w2+9⋅9w3+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
Multiply 9 by 9.
-6w2+9w-5+63w4+35w3-14w2+81w3+9w(5w)+9w⋅-2-7(9w2)-7(5w)-7⋅-2
Multiply w by w.
-6w2+9w-5+63w4+35w3-14w2+81w3+9⋅5w2+9w⋅-2-7(9w2)-7(5w)-7⋅-2
Multiply 9 by 5.
-6w2+9w-5+63w4+35w3-14w2+81w3+45w2+9w⋅-2-7(9w2)-7(5w)-7⋅-2
Multiply -2 by 9.
-6w2+9w-5+63w4+35w3-14w2+81w3+45w2-18w-7(9w2)-7(5w)-7⋅-2
Multiply 9 by -7.
-6w2+9w-5+63w4+35w3-14w2+81w3+45w2-18w-63w2-7(5w)-7⋅-2
Multiply 5 by -7.
-6w2+9w-5+63w4+35w3-14w2+81w3+45w2-18w-63w2-35w-7⋅-2
Multiply -7 by -2.
-6w2+9w-5+63w4+35w3-14w2+81w3+45w2-18w-63w2-35w+14
-6w2+9w-5+63w4+35w3-14w2+81w3+45w2-18w-63w2-35w+14
Add 35w3 and 81w3.
-6w2+9w-5+63w4+116w3-14w2+45w2-18w-63w2-35w+14
Add -14w2 and 45w2.
-6w2+9w-5+63w4+116w3+31w2-18w-63w2-35w+14
Subtract 63w2 from 31w2.
-6w2+9w-5+63w4+116w3-32w2-18w-35w+14
Subtract 35w from -18w.
-6w2+9w-5+63w4+116w3-32w2-53w+14
-6w2+9w-5+63w4+116w3-32w2-53w+14
Simplify by adding terms.
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Subtract 32w2 from -6w2.
-38w2+9w-5+63w4+116w3-53w+14
Subtract 53w from 9w.
-38w2-5+63w4+116w3-44w+14
Simplify the expression.
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Add -5 and 14.
-38w2+63w4+116w3-44w+9
Move -38w2.
63w4+116w3-38w2-44w+9
63w4+116w3-38w2-44w+9
63w4+116w3-38w2-44w+9
Simplify (-6w^2+9w-5)+(7w^2+9w-7)(9w^2+5w-2)

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