Question

Answer 1

\(15,x^4+2x^2+1=\left(x^2+1\right)^2\\ 16,4x^2-12xy+9y^2=\left(2x-3y\right)^2\\ 17,-x^2-2xy-y^2=-\left(x^2+2xy+y^2\right)=-\left(x+y\right)^2\\ 18,x^4+4-4x^2=\left(x^2-2\right)^2\\ 19,\left(x+y\right)^2-2\left(x+y\right)+1=\left(x+y-1\right)^2\\ 20,10x-x^2-25=-\left(x^2-10x+25\right)=-\left(x-5\right)^2\)

Answer 2

21: \(=\left(x-1\right)^3\)

22: \(=\left(x+2\right)^3\)

23: \(=x^2\left(x-1\right)-\left(x-1\right)=\left(x-1\right)^2\cdot\left(x+1\right)\)

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

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

\(=\left(x-y-5\right)\left(x+y+1\right)\)

25: \(=\left(x^2+1\right)\left(x^2+1\right)-3\left(x^2+1\right)=\left(x^2+1\right)\left(x^2-2\right)\)