Question

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

Answer 1

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

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 =(-m\±√(m^2-4nc))/(2n)`

Then the solutions are:

`a= (-(-5b)\±√((-5b)^2 -4(2)(2b^2)))/(2(2))\\\\a = (5b\±√(25b^2-16b^2))/(4)\\\\a = (5b\±3b)/(4)\\\\a_1=2b\\\\a_2 =(b)/(2)`

Finally The factored expression is:

`a-(b)/(2) = 0\\\\2a -b = 0\\\\`

and

`a-2b= 0`

Then

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