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

Question

plz help me solve!

Answer 1

The combo
(a+b)(a-b)
leads to a difference of squares
a^2 - b^2
This is a general pattern that will prove very useful later (not just in math)

In your problem

x^2 - 4y^2

You can always multiply it out by "distributing" one factor into the other (this trick always works).

(x-2y)(x+2y) =
x(x+2y) - 2y(x+2y) =
x^2 + 2xy -2xy -4y^2 =
x^2 - 4y^2

Answer 2

As an extract of what the person above explained,

x^2 - 4y^2

can also be represented as

x^2 - 2^2.y^2 (square root of 4 is 2. Also seen as 2*2 = 4)

which can be generally seen as:
(x-2y)^2


usually whenever you see an arrangement like that with the same numbers but with different signs, the answer is the overal square of of the one that has the minus sign.

Answer 3

By the rule: (a+b)(a-b) = a^2 -b^2

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

Answer 4

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