Evaluate
-\frac{11x^{2}}{2}+5x+\frac{1}{2}
Expand
-\frac{11x^{2}}{2}+5x+\frac{1}{2}
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\frac{1}{2}\left(x^{2}-2x+1\right)+6x\left(1-x\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.
\frac{1}{2}x^{2}-x+\frac{1}{2}+6x\left(1-x\right)
Use the distributive property to multiply \frac{1}{2} by x^{2}-2x+1.
\frac{1}{2}x^{2}-x+\frac{1}{2}+6x-6x^{2}
Use the distributive property to multiply 6x by 1-x.
\frac{1}{2}x^{2}+5x+\frac{1}{2}-6x^{2}
Combine -x and 6x to get 5x.
-\frac{11}{2}x^{2}+5x+\frac{1}{2}
Combine \frac{1}{2}x^{2} and -6x^{2} to get -\frac{11}{2}x^{2}.
\frac{1}{2}\left(x^{2}-2x+1\right)+6x\left(1-x\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.
\frac{1}{2}x^{2}-x+\frac{1}{2}+6x\left(1-x\right)
Use the distributive property to multiply \frac{1}{2} by x^{2}-2x+1.
\frac{1}{2}x^{2}-x+\frac{1}{2}+6x-6x^{2}
Use the distributive property to multiply 6x by 1-x.
\frac{1}{2}x^{2}+5x+\frac{1}{2}-6x^{2}
Combine -x and 6x to get 5x.
-\frac{11}{2}x^{2}+5x+\frac{1}{2}
Combine \frac{1}{2}x^{2} and -6x^{2} to get -\frac{11}{2}x^{2}.
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