how would this be factorised? 4x^2-16?

remember this ok???i mean always...

(a - b)(a + b) = a² - b²

ok???

now, back 2 your question, 4x^2 - 16

it can be factored out first by 4

so,,, 4(x^2 - 4)

ok??next, use the formula, (a - b)(a + b) = a² - b²

4(sqrtx^2 - sqrt4)(sqrtx^2 + sqrt4)

which is 4(x - 2)(x + 2)

that is the answer!!!

good luck!

4x^2 - 16
= 4(x^2 - 4)
= 4(x^2 + 2x - 2x - 4)
= 4(x + 2)(x - 2)

(2x+4)(2x-4)

4 (x² - 4)
4 (x - 2)(x + 2)

That is called the difference of squares.
A²-B²=(A+B)(A-B)

₪ ɦəlʞɹɐq ₪

It's a difference of squares. These are very cool little equations, because, when everything is a perfect square like that, in a second degree binomial, you can simply take the square root of each: 2, x, and 4, and write:

(2x+4)(2x-4)

pull a 2 out of each

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

Group your terms.

4(x+2)(x-2)

Quick and easy, if you know how to solve perfect squares.

Let's do a check. Let x=3

Original equation:

4(3)^2 -16 = ?
4(9) -16 =?
36-16=20

And the simplified equation:

4((3)+2)((3)-2)
4(5)(1) = ?

4(5) = 20

It works.

First, a spelling tip: "squared" instead of "squered"

This binomial is the difference of two squares. Both 4x^2 and 16 are, individually, perfect squares:
4x^2 = (2x)(2x)
16 = (4)(4)

There is a formula you should remember for factoring when you are given the difference of two squares:
a² - b² = (a - b)(a + b)

Since a = 2x, and b = 4, this means that the binomial can be factored as:
(2x - 4)(2x + 4)

(2x - 4)(2x + 4)