How do you solve x squared minus 4 y squared?

Answer 1

x^(2) - 4y^(2)

Before calculating , we note

#1 ' There is a negative sign between the two squares. So it will factor

#2 ' '4' is the square of '2' . So we can redraw the terms as ( 2y)^2

Hence

x^(2) - (2y)^2)

This now satisfies the two conditions above. . So it will factor to

( x - 2y)(x + 2y)

Note the different signs in each bracket .

You hve asked for it to be solved!!! To solve you need to equate the terms to a value. In this case use '0'

Hence

(x - 2y)(x + 2y) = 0

Taking each bracket in turn

x - 2y = 0

x = 2y or 2 = x/y or y = x/2

Then

x + 2y = 0

x = -2y or -2/x/y or y = x/-2

Are the possible forms of solution.

NB If you have two squared terms and a positive (+) between them, then it does NOT factor.

NNB Think of the Pythagorean Equation

a^2 + b^2 = h^2 This DOES NOT factor.

However

a^2 = h^2 - b^2 (Algebraic rearrangement) , DOES factor to

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

Answer 2

It is not clear what you want to solve for.