5: \(=4b^2-2b+\dfrac{1}{4}-\dfrac{1}{4}+a-a^2\)
\(=\left(2b\right)^2-2\cdot2b\cdot\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2-\left(a^2-a+\dfrac{1}{4}\right)\)
\(=\left(2b-\dfrac{1}{2}\right)^2-\left(a-\dfrac{1}{2}\right)^2\)
\(=\left(2b-\dfrac{1}{2}-a+\dfrac{1}{2}\right)\left(2b-\dfrac{1}{2}+a-\dfrac{1}{2}\right)\)
\(=\left(2b-a\right)\left(2b+a-1\right)\)
6:
\(=b^2-4b+4-9c^2\)
\(=\left(b-2\right)^2-9c^2\)
\(=\left(b-2-3c\right)\left(b-2+3c\right)\)
5) \(4b^2-2b+a-a^2\)
\(=\left(2b-a\right)\left(2b+a\right)-\left(2b-a\right)\)
\(=\left(2b-a\right)\left(2b+a-1\right)\)
6) \(b^2-9c^2+4+4b\)
\(=\left(b+2\right)^2-9c^2\)
\(=\left(b+3c+2\right)\left(b-3c+2\right)\)
