Evaluate
\frac{161x^{2}}{100}-15x+26
Expand
\frac{161x^{2}}{100}-15x+26
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\frac{9}{4}x^{2}-15x+25-\left(\frac{4}{5}x-1\right)\left(\frac{4}{5}x+1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{3}{2}x-5\right)^{2}.
\frac{9}{4}x^{2}-15x+25-\left(\left(\frac{4}{5}x\right)^{2}-1\right)
Consider \left(\frac{4}{5}x-1\right)\left(\frac{4}{5}x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.
\frac{9}{4}x^{2}-15x+25-\left(\left(\frac{4}{5}\right)^{2}x^{2}-1\right)
Expand \left(\frac{4}{5}x\right)^{2}.
\frac{9}{4}x^{2}-15x+25-\left(\frac{16}{25}x^{2}-1\right)
Calculate \frac{4}{5} to the power of 2 and get \frac{16}{25}.
\frac{9}{4}x^{2}-15x+25-\frac{16}{25}x^{2}+1
To find the opposite of \frac{16}{25}x^{2}-1, find the opposite of each term.
\frac{161}{100}x^{2}-15x+25+1
Combine \frac{9}{4}x^{2} and -\frac{16}{25}x^{2} to get \frac{161}{100}x^{2}.
\frac{161}{100}x^{2}-15x+26
Add 25 and 1 to get 26.
\frac{9}{4}x^{2}-15x+25-\left(\frac{4}{5}x-1\right)\left(\frac{4}{5}x+1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{3}{2}x-5\right)^{2}.
\frac{9}{4}x^{2}-15x+25-\left(\left(\frac{4}{5}x\right)^{2}-1\right)
Consider \left(\frac{4}{5}x-1\right)\left(\frac{4}{5}x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.
\frac{9}{4}x^{2}-15x+25-\left(\left(\frac{4}{5}\right)^{2}x^{2}-1\right)
Expand \left(\frac{4}{5}x\right)^{2}.
\frac{9}{4}x^{2}-15x+25-\left(\frac{16}{25}x^{2}-1\right)
Calculate \frac{4}{5} to the power of 2 and get \frac{16}{25}.
\frac{9}{4}x^{2}-15x+25-\frac{16}{25}x^{2}+1
To find the opposite of \frac{16}{25}x^{2}-1, find the opposite of each term.
\frac{161}{100}x^{2}-15x+25+1
Combine \frac{9}{4}x^{2} and -\frac{16}{25}x^{2} to get \frac{161}{100}x^{2}.
\frac{161}{100}x^{2}-15x+26
Add 25 and 1 to get 26.
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Limits
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