Factor -20p(3p-2)^2-20(3p-2)p-5p

Math
-20p(3p-2)2-20(3p-2)p-5p
Factor -5p out of -20p(3p-2)2-20(3p-2)p-5p.
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Move 3p-2.
-20p(3p-2)2-20p(3p-2)-5p
Factor -5p out of -20p(3p-2)2.
-5p(4(3p-2)2)-20p(3p-2)-5p
Factor -5p out of -20p(3p-2).
-5p(4(3p-2)2)-5p(4(3p-2))-5p
Factor -5p out of -5p.
-5p(4(3p-2)2)-5p(4(3p-2))-5p(1)
Factor -5p out of -5p(4(3p-2)2)-5p(4(3p-2)).
-5p(4(3p-2)2+4(3p-2))-5p(1)
Factor -5p out of -5p(4(3p-2)2+4(3p-2))-5p(1).
-5p(4(3p-2)2+4(3p-2)+1)
-5p(4(3p-2)2+4(3p-2)+1)
Let u=3p-2. Substitute u for all occurrences of 3p-2.
-5p(4u2+4u+1)
Factor using the perfect square rule.
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Rewrite 4u2 as (2u)2.
-5p((2u)2+4u+1)
Rewrite 1 as 12.
-5p((2u)2+4u+12)
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
4u=2⋅(2u)⋅1
Rewrite the polynomial.
-5p((2u)2+2⋅(2u)⋅1+12)
Factor using the perfect square trinomial rule a2+2ab+b2=(a+b)2, where a=2u and b=1.
-5p(2u+1)2
-5p(2u+1)2
Replace all occurrences of u with 3p-2.
-5p(2(3p-2)+1)2
Simplify.
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Simplify each term.
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Apply the distributive property.
-5p(2(3p)+2⋅-2+1)2
Multiply 3 by 2.
-5p(6p+2⋅-2+1)2
Multiply 2 by -2.
-5p(6p-4+1)2
-5p(6p-4+1)2
Add -4 and 1.
-5p(6p-3)2
-5p(6p-3)2
Factor 3 out of 6p-3.
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Factor 3 out of 6p.
-5p(3(2p)-3)2
Factor 3 out of -3.
-5p(3(2p)+3(-1))2
Factor 3 out of 3(2p)+3(-1).
-5p(3(2p-1))2
-5p(3(2p-1))2
Factor.
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Apply the product rule to 3(2p-1).
-5p(32(2p-1)2)
Remove unnecessary parentheses.
-5p⋅32(2p-1)2
-5p⋅32(2p-1)2
Factor -20p(3p-2)^2-20(3p-2)p-5p

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