how do you factor this equation?

Factor it to g2 65 !i

a^2 - b^2 = (a + b)(a - b)

1/4x^2 - 4/9
= 1/4x^2 + 2/6x - 2/6x - 4/9
= (1/2x)^2 + 2/6x - 2/6x - (2/3)^2
= [(1/2x)^2 + 2/6x] - [2/6x + (2/3)^2]
= 1/2x[1/2x + 1/3] - 2/3[1/2x + 2/3]
= [1/2x + 2/3][1/2x - 2/3]

even though there are fractions, it's still just a a sq - sq, so
(1/2x+2/3)(1/2x-2/3)

if it were x^2-4, would you know how to do that (x-2)(x+2)? Same thing.

well 1/4 squared is the same as 1/4 to the second power so...um srry i dont know all i know is that squared means 2nd power im only in 6th grade

you need to make better use of brackets.

(1/4) x ² - 4/9
(1/4) [ x ² - 16/9 ]
(1/4) [ (x - 4/3) (x + 4/3) ]

I think you meant:

(1/4)x^2 - 4/9

That symbol, "^", is used to mean "raised to the power of", so in this case it means to the power of 2, which means "squared".

4/9 is also (2/3)^2.

This is one of those factoring things you just memorize. If you have the the product of a variable that is squared and a constant, minus another constant, then the factors are always the product of: the quantity of the square root of the variable and first constant, plus the square root of the second constant; times the quantity of the square root of the variable -minus- the square root of the second variable.

Like this:

4x^2 - 16 factors to:
(2x+4)(2x-4)

This holds true for fractions, too.

If you did really mean (1/4)x^2 - 4/9, then:

The square root of a fraction is found by finding the square roots of the numerator and denominator. That simple.

So the square root of 1/4 is 1/2, and the square root of 4/9 is 2/3.

Therefore:
((1/2)x+2/3)((1/2)x-2/3)


Multiply to test:
(1/4)x^2 - (2/6)x + (2/6)x - 4/9 Add, the -(2/6)x and +(2/6)x cancel:
(1/4)x^2 - 4/9 Therefore the factor is correct.


If you meant 1/(4x^2) - 4/9, then:

(1/(2x)+2/3)(1/(2x)-2/3)

It can be a bit of a challenge typing in an equation into plain text, but it is an essential skill in communicating questions and results.

(1/2x+2/3) (1/2x-2/3)

Factor
(1/2 x - 2/3)(1/2 x + 2/3)


Hope this helps you! Please email for further clarification.