B2: a) \(\left(x+\dfrac{1}{2}\right)\left(\dfrac{1}{2}-x\right)\)

\(=-\left(x+\dfrac{1}{2}\right)\left(x-\dfrac{1}{2}\right)\)

\(=-x^2+\dfrac{1}{4}\)

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

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

\(=9x^2-4y^2\)

c) \(\left(x-3\right)\left(3+x\right)\)

\(=x^2-3^2\)

\(=x^2-9\)

d) \(x^2+6x+9\)

\(=x^2+2\cdot3\cdot x+3^2\)

\(=\left(x+3\right)^2\)

e) \(9x^2-6x+1\)

\(=\left(3x\right)^2-2\cdot3x\cdot1+1^2\)

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

f) \(x^2y^2+xy+\dfrac{1}{4}\)

\(=\left(xy\right)^2+2\cdot\dfrac{1}{2}\cdot xy+\left(\dfrac{1}{2}\right)^2\)

\(=\left(xy+\dfrac{1}{2}\right)^2\)

g) \(\left(x-y\right)^2+6\left(x-y\right)+9\)

\(=\left(x-y\right)^2+2\cdot3\cdot\left(x-y\right)+3^2\)

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

h) \(x^2+8x+16\)

\(=x^2+2\cdot4\cdot x+4^2\)

\(=\left(x+4\right)^2\)

i) \(9x^2-24x+16\)

\(=\left(3x\right)^2-2\cdot3x\cdot4+4^2\)

\(=\left(3x-4\right)^2\)

k) \(x^2-3x+\dfrac{9}{4}\)

\(=x^2-2\cdot\dfrac{3}{2}\cdot x+\left(\dfrac{3}{2}\right)^2\)

\(=\left(x-\dfrac{3}{2}\right)^2\)

l) \(4x^2y^4-4xy^3+y^2\)

\(=\left(2xy^2\right)^2-2\cdot2xy^2\cdot y+y^2\)

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

m) \(9x^2-6x+1\)

\(=\left(3x\right)^2-2\cdot3x\cdot1+1\)

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

Thank you very much Phong