Question

Answer 1

\(a,x^2+5x+\dfrac{25}{4}=x^2+5x+\left(\dfrac{5}{2}\right)^2=\left(x+\dfrac{5}{2}\right)^2.\\ b,16x^2-8x+1=\left(4x-1\right)^2.\\ c,4x^2+12xy+9y^2=\left(2x+3y\right)^2.\)

 

Answer 2

d: \(=\left(x^2+9x+18\right)\left(x^2+9x+20\right)+1\)

\(=\left(x^2+9x\right)^2+38\left(x^2+9x\right)+360+1\)

\(=\left(x^2+9x+19\right)^2\)

e: \(=x^2+2x+1+y^2+2y+1+2\left(x+1\right)\left(y+1\right)\)

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

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