Question

Answer 1

2:

a: \(4x\left(x-2y\right)-8y\cdot\left(x-2y\right)\)

\(=\left(x-2y\right)\left(4x-8y\right)\)

\(=4\left(x-2y\right)^2\)

b: \(-25x^2y^2+10xy-1\)

\(=-\left(25x^2y^2-10xy+1\right)\)

\(=-\left(5xy-1\right)^2\)

c: \(x^2+x^3+xy-y^3+y^2\)

\(=\left(x^3-y^3\right)+\left(x^2+xy+y^2\right)\)

\(=\left(x-y\right)\left(x^2+xy+y^2\right)+\left(x^2+xy+y^2\right)\)

\(=\left(x^2+xy+y^2\right)\left(x-y+1\right)\)

5:

\(a^2+b^2+c^2=ab+bc+ac\)

=>\(2a^2+2b^2+2c^2=2ab+2ac+2bc\)

=>\(\left(a^2-2ab+b^2\right)+\left(a^2-2ac+c^2\right)+\left(b^2-2bc+c^2\right)=0\)

=>\(\left(a-b\right)^2+\left(b-c\right)^2+\left(a-c\right)^2=0\)

=>a=b=c