Simplify 9*((1-c)^2)-45/4*(1/2*(c^2+1)+3/19*(1-c)^2)

Math
9⋅((1-c)2)-454⋅(12⋅(c2+1)+319⋅(1-c)2)
Simplify each term.
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Rewrite (1-c)2 as (1-c)(1-c).
9⋅((1-c)(1-c))-454⋅(12⋅(c2+1)+319⋅(1-c)2)
Expand (1-c)(1-c) using the FOIL Method.
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Apply the distributive property.
9⋅(1(1-c)-c(1-c))-454⋅(12⋅(c2+1)+319⋅(1-c)2)
Apply the distributive property.
9⋅(1⋅1+1(-c)-c(1-c))-454⋅(12⋅(c2+1)+319⋅(1-c)2)
Apply the distributive property.
9⋅(1⋅1+1(-c)-c⋅1-c(-c))-454⋅(12⋅(c2+1)+319⋅(1-c)2)
9⋅(1⋅1+1(-c)-c⋅1-c(-c))-454⋅(12⋅(c2+1)+319⋅(1-c)2)
Simplify and combine like terms.
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Simplify each term.
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Multiply 1 by 1.
9⋅(1+1(-c)-c⋅1-c(-c))-454⋅(12⋅(c2+1)+319⋅(1-c)2)
Multiply -c by 1.
9⋅(1-c-c⋅1-c(-c))-454⋅(12⋅(c2+1)+319⋅(1-c)2)
Multiply -1 by 1.
9⋅(1-c-c-c(-c))-454⋅(12⋅(c2+1)+319⋅(1-c)2)
Multiply c by c.
9⋅(1-c-c-1⋅-1c2)-454⋅(12⋅(c2+1)+319⋅(1-c)2)
Multiply -1 by -1.
9⋅(1-c-c+1c2)-454⋅(12⋅(c2+1)+319⋅(1-c)2)
Multiply c2 by 1.
9⋅(1-c-c+c2)-454⋅(12⋅(c2+1)+319⋅(1-c)2)
9⋅(1-c-c+c2)-454⋅(12⋅(c2+1)+319⋅(1-c)2)
Subtract c from -c.
9⋅(1-2c+c2)-454⋅(12⋅(c2+1)+319⋅(1-c)2)
9⋅(1-2c+c2)-454⋅(12⋅(c2+1)+319⋅(1-c)2)
Apply the distributive property.
9⋅1+9(-2c)+9c2-454⋅(12⋅(c2+1)+319⋅(1-c)2)
Simplify.
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Multiply 9 by 1.
9+9(-2c)+9c2-454⋅(12⋅(c2+1)+319⋅(1-c)2)
Multiply -2 by 9.
9-18c+9c2-454⋅(12⋅(c2+1)+319⋅(1-c)2)
9-18c+9c2-454⋅(12⋅(c2+1)+319⋅(1-c)2)
Simplify each term.
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Apply the distributive property.
9-18c+9c2-454⋅(12c2+12⋅1+319⋅(1-c)2)
Combine 12 and c2.
9-18c+9c2-454⋅(c22+12⋅1+319⋅(1-c)2)
Multiply 12 by 1.
9-18c+9c2-454⋅(c22+12+319⋅(1-c)2)
Rewrite (1-c)2 as (1-c)(1-c).
9-18c+9c2-454⋅(c22+12+319⋅((1-c)(1-c)))
Expand (1-c)(1-c) using the FOIL Method.
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Apply the distributive property.
9-18c+9c2-454⋅(c22+12+319⋅(1(1-c)-c(1-c)))
Apply the distributive property.
9-18c+9c2-454⋅(c22+12+319⋅(1⋅1+1(-c)-c(1-c)))
Apply the distributive property.
9-18c+9c2-454⋅(c22+12+319⋅(1⋅1+1(-c)-c⋅1-c(-c)))
9-18c+9c2-454⋅(c22+12+319⋅(1⋅1+1(-c)-c⋅1-c(-c)))
Simplify and combine like terms.
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Simplify each term.
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Multiply 1 by 1.
9-18c+9c2-454⋅(c22+12+319⋅(1+1(-c)-c⋅1-c(-c)))
Multiply -c by 1.
9-18c+9c2-454⋅(c22+12+319⋅(1-c-c⋅1-c(-c)))
Multiply -1 by 1.
9-18c+9c2-454⋅(c22+12+319⋅(1-c-c-c(-c)))
Multiply c by c.
9-18c+9c2-454⋅(c22+12+319⋅(1-c-c-1⋅-1c2))
Multiply -1 by -1.
9-18c+9c2-454⋅(c22+12+319⋅(1-c-c+1c2))
Multiply c2 by 1.
9-18c+9c2-454⋅(c22+12+319⋅(1-c-c+c2))
9-18c+9c2-454⋅(c22+12+319⋅(1-c-c+c2))
Subtract c from -c.
9-18c+9c2-454⋅(c22+12+319⋅(1-2c+c2))
9-18c+9c2-454⋅(c22+12+319⋅(1-2c+c2))
Apply the distributive property.
9-18c+9c2-454⋅(c22+12+319⋅1+319(-2c)+319c2)
Simplify.
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Multiply 319 by 1.
9-18c+9c2-454⋅(c22+12+319+319(-2c)+319c2)
Multiply 319(-2c).
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Combine -2 and 319.
9-18c+9c2-454⋅(c22+12+319+-2⋅319c+319c2)
Multiply -2 by 3.
9-18c+9c2-454⋅(c22+12+319+-619c+319c2)
Combine -619 and c.
9-18c+9c2-454⋅(c22+12+319+-6c19+319c2)
9-18c+9c2-454⋅(c22+12+319+-6c19+319c2)
Combine 319 and c2.
9-18c+9c2-454⋅(c22+12+319+-6c19+3c219)
9-18c+9c2-454⋅(c22+12+319+-6c19+3c219)
Move the negative in front of the fraction.
9-18c+9c2-454⋅(c22+12+319-6c19+3c219)
9-18c+9c2-454⋅(c22+12+319-6c19+3c219)
To write c22 as a fraction with a common denominator, multiply by 1919.
9-18c+9c2-454⋅(12+319-6c19+c22⋅1919+3c219)
To write 3c219 as a fraction with a common denominator, multiply by 22.
9-18c+9c2-454⋅(12+319-6c19+c22⋅1919+3c219⋅22)
Write each expression with a common denominator of 38, by multiplying each by an appropriate factor of 1.
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Multiply c22 and 1919.
9-18c+9c2-454⋅(12+319-6c19+c2⋅192⋅19+3c219⋅22)
Multiply 2 by 19.
9-18c+9c2-454⋅(12+319-6c19+c2⋅1938+3c219⋅22)
Multiply 3c219 and 22.
9-18c+9c2-454⋅(12+319-6c19+c2⋅1938+3c2⋅219⋅2)
Multiply 19 by 2.
9-18c+9c2-454⋅(12+319-6c19+c2⋅1938+3c2⋅238)
9-18c+9c2-454⋅(12+319-6c19+c2⋅1938+3c2⋅238)
Combine the numerators over the common denominator.
9-18c+9c2-454⋅(12+319-6c19+c2⋅19+3c2⋅238)
Simplify each term.
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Simplify the numerator.
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Factor c2 out of c2⋅19+3c2⋅2.
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Factor c2 out of c2⋅19.
9-18c+9c2-454⋅(12+319-6c19+c2(19)+3c2⋅238)
Factor c2 out of 3c2⋅2.
9-18c+9c2-454⋅(12+319-6c19+c2(19)+c2(3⋅2)38)
Factor c2 out of c2(19)+c2(3⋅2).
9-18c+9c2-454⋅(12+319-6c19+c2(19+3⋅2)38)
9-18c+9c2-454⋅(12+319-6c19+c2(19+3⋅2)38)
Multiply 3 by 2.
9-18c+9c2-454⋅(12+319-6c19+c2(19+6)38)
Add 19 and 6.
9-18c+9c2-454⋅(12+319-6c19+c2⋅2538)
9-18c+9c2-454⋅(12+319-6c19+c2⋅2538)
Move 25 to the left of c2.
9-18c+9c2-454⋅(12+319-6c19+25c238)
9-18c+9c2-454⋅(12+319-6c19+25c238)
To write 12 as a fraction with a common denominator, multiply by 1919.
9-18c+9c2-454⋅(12⋅1919+319-6c19+25c238)
To write 319 as a fraction with a common denominator, multiply by 22.
9-18c+9c2-454⋅(12⋅1919+319⋅22-6c19+25c238)
Write each expression with a common denominator of 38, by multiplying each by an appropriate factor of 1.
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Multiply 12 and 1919.
9-18c+9c2-454⋅(192⋅19+319⋅22-6c19+25c238)
Multiply 2 by 19.
9-18c+9c2-454⋅(1938+319⋅22-6c19+25c238)
Multiply 319 and 22.
9-18c+9c2-454⋅(1938+3⋅219⋅2-6c19+25c238)
Multiply 19 by 2.
9-18c+9c2-454⋅(1938+3⋅238-6c19+25c238)
9-18c+9c2-454⋅(1938+3⋅238-6c19+25c238)
Combine the numerators over the common denominator.
9-18c+9c2-454⋅(19+3⋅238-6c19+25c238)
Simplify the numerator.
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Multiply 3 by 2.
9-18c+9c2-454⋅(19+638-6c19+25c238)
Add 19 and 6.
9-18c+9c2-454⋅(2538-6c19+25c238)
9-18c+9c2-454⋅(2538-6c19+25c238)
Apply the distributive property.
9-18c+9c2-454⋅2538-454(-6c19)-454⋅25c238
Simplify.
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Multiply -454⋅2538.
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Multiply 2538 and 454.
9-18c+9c2-25⋅4538⋅4-454(-6c19)-454⋅25c238
Multiply 25 by 45.
9-18c+9c2-112538⋅4-454(-6c19)-454⋅25c238
Multiply 38 by 4.
9-18c+9c2-1125152-454(-6c19)-454⋅25c238
9-18c+9c2-1125152-454(-6c19)-454⋅25c238
Cancel the common factor of 2.
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Move the leading negative in -454 into the numerator.
9-18c+9c2-1125152+-454(-6c19)-454⋅25c238
Move the leading negative in -6c19 into the numerator.
9-18c+9c2-1125152+-454⋅-6c19-454⋅25c238
Factor 2 out of 4.
9-18c+9c2-1125152+-452(2)⋅-6c19-454⋅25c238
Factor 2 out of -6c.
9-18c+9c2-1125152+-452(2)⋅2(-3c)19-454⋅25c238
Cancel the common factor.
9-18c+9c2-1125152+-452⋅2⋅2(-3c)19-454⋅25c238
Rewrite the expression.
9-18c+9c2-1125152+-452⋅-3c19-454⋅25c238
9-18c+9c2-1125152+-452⋅-3c19-454⋅25c238
Multiply -452 and -3c19.
9-18c+9c2-1125152+-45(-3c)2⋅19-454⋅25c238
Multiply -3 by -45.
9-18c+9c2-1125152+135c2⋅19-454⋅25c238
Multiply 2 by 19.
9-18c+9c2-1125152+135c38-454⋅25c238
Multiply -454⋅25c238.
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Multiply 25c238 and 454.
9-18c+9c2-1125152+135c38-25c2⋅4538⋅4
Multiply 45 by 25.
9-18c+9c2-1125152+135c38-1125c238⋅4
Multiply 38 by 4.
9-18c+9c2-1125152+135c38-1125c2152
9-18c+9c2-1125152+135c38-1125c2152
9-18c+9c2-1125152+135c38-1125c2152
9-18c+9c2-1125152+135c38-1125c2152
To write 9 as a fraction with a common denominator, multiply by 152152.
-18c+9c2+9⋅152152-1125152+135c38-1125c2152
Combine 9 and 152152.
-18c+9c2+9⋅152152-1125152+135c38-1125c2152
Combine the numerators over the common denominator.
-18c+9c2+9⋅152-1125152+135c38-1125c2152
Simplify the numerator.
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Multiply 9 by 152.
-18c+9c2+1368-1125152+135c38-1125c2152
Subtract 1125 from 1368.
-18c+9c2+243152+135c38-1125c2152
-18c+9c2+243152+135c38-1125c2152
To write -18c as a fraction with a common denominator, multiply by 3838.
9c2+243152-18c⋅3838+135c38-1125c2152
Simplify terms.
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Combine -18c and 3838.
9c2+243152+-18c⋅3838+135c38-1125c2152
Combine the numerators over the common denominator.
9c2+243152+-18c⋅38+135c38-1125c2152
9c2+243152+-18c⋅38+135c38-1125c2152
Simplify each term.
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Simplify the numerator.
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Factor 9c out of -18c⋅38+135c.
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Factor 9c out of -18c⋅38.
9c2+243152+9c(-2⋅38)+135c38-1125c2152
Factor 9c out of 135c.
9c2+243152+9c(-2⋅38)+9c(15)38-1125c2152
Factor 9c out of 9c(-2⋅38)+9c(15).
9c2+243152+9c(-2⋅38+15)38-1125c2152
9c2+243152+9c(-2⋅38+15)38-1125c2152
Multiply -2 by 38.
9c2+243152+9c(-76+15)38-1125c2152
Add -76 and 15.
9c2+243152+9c⋅-6138-1125c2152
9c2+243152+9c⋅-6138-1125c2152
Multiply -61 by 9.
9c2+243152+-549c38-1125c2152
Move the negative in front of the fraction.
9c2+243152-549c38-1125c2152
9c2+243152-549c38-1125c2152
To write 9c2 as a fraction with a common denominator, multiply by 152152.
243152-549c38+9c2⋅152152-1125c2152
Simplify terms.
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Combine 9c2 and 152152.
243152-549c38+9c2⋅152152-1125c2152
Combine the numerators over the common denominator.
243152-549c38+9c2⋅152-1125c2152
243152-549c38+9c2⋅152-1125c2152
Simplify the numerator.
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Factor 9c2 out of 9c2⋅152-1125c2.
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Factor 9c2 out of 9c2⋅152.
243152-549c38+9c2(152)-1125c2152
Factor 9c2 out of -1125c2.
243152-549c38+9c2(152)+9c2(-125)152
Factor 9c2 out of 9c2(152)+9c2(-125).
243152-549c38+9c2(152-125)152
243152-549c38+9c2(152-125)152
Subtract 125 from 152.
243152-549c38+9c2⋅27152
Multiply 27 by 9.
243152-549c38+243c2152
243152-549c38+243c2152
Simplify 9*((1-c)^2)-45/4*(1/2*(c^2+1)+3/19*(1-c)^2)

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