MATH SOLVE

3 months ago

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

Accepted Solution

A:

Answer:[tex](2a-b)(a-2b) = 0[/tex]Step-by-step explanation:We can use the quadratic formula to factor this expressionFor 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]