a: \(17^2+13^2+26\cdot17\)
\(=17^2+2\cdot17\cdot13+13^2\)
\(=\left(17+13\right)^2=30^2=900\)
b: \(27\cdot875+270\cdot12,5\)
\(=27\cdot875+27\cdot125\)
\(=27\left(875+125\right)=27\cdot1000=27000\)
c: \(77^2+12^2-24\cdot77\)
\(=77^2-2\cdot77\cdot12+12^2\)
\(=\left(77-12\right)^2=65^2=4225\)
d: \(x^2-10x+25\)
\(=x^2-2\cdot x\cdot5+5^2\)
\(=\left(x-5\right)^2=\left(-90-5\right)^2=\left(-95\right)^2=9025\)
e: \(67^2-33^2\)
\(=\left(67-33\right)\left(67+33\right)\)
\(=34\cdot100=3400\)
g: \(100^2-99^2+98^2-97^2+\cdots+6^2-5^2\)
=(100-99)(100+99)+(98-97)(98+97)+...+(6-5)(6+5)
=100+99+98+97+...+6+5
\(=\left(100-5+1\right)\cdot\frac{\left(100+5\right)}{2}=96\cdot\frac{105}{2}=48\cdot105=5040\)
i: \(A=x^2+2xy+y^2\)
\(=\left(x+y\right)^2\)
\(=1^2=1\)
