Answer:
[tex](2a-b)(a-2b) = 0[/tex]
Step-by-step explanation:
We can use the quadratic formula to factor this expression
For a quadratic function of the form:
[tex]na ^ 2 + ma + c[/tex]
Whe have:
[tex]2a^2 + 2b^2 - 5ab[/tex]
Then:
[tex]n = 2\\\\m = -5b\\\\c = 2b^2[/tex]
The quadratic formula is:
[tex]a =\frac{-m\±\sqrt{m^2-4nc}}{2n}[/tex]
Then the solutions are:
[tex]a= \frac{-(-5b)\±\sqrt{(-5b)^2 -4(2)(2b^2)}}{2(2)}\\\\a = \frac{5b\±\sqrt{25b^2-16b^2}}{4}\\\\a = \frac{5b\±3b}{4}\\\\a_1=2b\\\\a_2 =\frac{b}{2}[/tex]
Finally The factored expression is:
[tex]a-\frac{b}{2} = 0\\\\2a -b = 0\\\\[/tex]
and
[tex]a-2b= 0[/tex]
Then
[tex]2a^2 + 2b^2 - 5ab = (2a-b)(a-2b) = 0[/tex]
