Remove parentheses.
\[4x\times 2+4bx-aa+bb=0\]
Simplify \(4x\times 2\) to \(8x\).
\[8x+4bx-aa+bb=0\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[8x+4bx-{a}^{2}+bb=0\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[8x+4bx-{a}^{2}+{b}^{2}=0\]
Add \({a}^{2}\) to both sides.
\[8x+4bx+{b}^{2}={a}^{2}\]
Move all terms to one side.
\[8x+4bx+{b}^{2}-{a}^{2}=0\]
Subtract \({b}^{2}\) from both sides.
\[8x+4bx-{a}^{2}=-{b}^{2}\]
Add \({a}^{2}\) to both sides.
\[8x+4bx=-{b}^{2}+{a}^{2}\]
Regroup terms.
\[8x+4bx={a}^{2}-{b}^{2}\]
Factor out the common term \(4x\).
\[4x(2+b)={a}^{2}-{b}^{2}\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[4x(2+b)=(a+b)(a-b)\]
Divide both sides by \(4\).
\[x(2+b)=\frac{(a+b)(a-b)}{4}\]
Divide both sides by \(2+b\).
\[x=\frac{\frac{(a+b)(a-b)}{4}}{2+b}\]
Simplify \(\frac{\frac{(a+b)(a-b)}{4}}{2+b}\) to \(\frac{(a+b)(a-b)}{4(2+b)}\).
\[x=\frac{(a+b)(a-b)}{4(2+b)}\]
x=((a+b)*(a-b))/(4*(2+b))
