Question

Factor completely, then place the factors in the proper location on the grid. 2a 2 + 2b 2 - 5ab

Answer 1

Answer:

$(2a-b)(a-2b) = 0$

Step-by-step explanation:

We can use the quadratic formula to factor this expression

For a quadratic function of the form:

$na ^ 2 + ma + c$

Whe have:

$2a^2 + 2b^2 - 5ab$

Then:

$n = 2\\\\m = -5b\\\\c = 2b^2$

The quadratic formula is:

$a =\frac{-m\±\sqrt{m^2-4nc}}{2n}$

Then the solutions are:

$a= \frac{-(-5b)\±\sqrt{(-5b)^2 -4(2)(2b^2)}}{2(2)}\\\\a = \frac{5b\±\sqrt{25b^2-16b^2}}{4}\\\\a = \frac{5b\±3b}{4}\\\\a_1=2b\\\\a_2 =\frac{b}{2}$

Finally The factored expression is:

$a-\frac{b}{2} = 0\\\\2a -b = 0$

and

$a-2b= 0$

Then

$2a^2 + 2b^2 - 5ab = (2a-b)(a-2b) = 0$