Need help asap please!
Write the expression as a binomial
x^2-4/9x+4/81

Question

Need help asap please!
Write the expression as a binomial
x^2-4/9x+4/81

mathstudent55 · Answer

You mean this expression?

$x^2 - \dfrac{4}{9}x + \dfrac{4}{81} $

anonymous · Answer

yes :) @mathstudent55 
well the x is next to only the 9

mathstudent55 · Answer

Notice that x^2 is the square of x. Also, 4/81 is the square of 2/9.
This could well be the square of a binomial.

mathstudent55 · Answer

If it is the square of the binomial, then you'd have and x from the x^2 and a 2/9 from the 4/81. Since the sign of the x term is negative, you'd have a minus sign.

$(x - \dfrac{2}{9} )^2 $

All you need to do is square the binomial and see if the middle term of your given trinomial fits in.

mathstudent55 · Answer

When you square a binomial you do this:

$ (a - b)^2 = a^2 - 2ab + b^2$

We already know that the x^2 term and the number at the end fit in.
Let's check the middle term.

$-2ab = -2(x)(\dfrac{2}{9}) = -\dfrac{4}{9}x$

The middle term checks out, so you can conclude that

$x^2 - \dfrac{4}{9}x + \dfrac{4}{81} = (x - \dfrac{2}{9} )^2$

anonymous · Answer

Thank you so much! :) @mathstudent55

mathstudent55 · Answer

You're welcome.