Question

Difference in two squares. factorize this 9x⁴-16y²?​

Answer 1

(3x²+4y)(3x²-4y)

Explanation:

"difference in two squares" is the formula where a²-b²=(a-b)(a+b)

So we need to apply that formula to
`9x^(4)`-16y², where
`9x^(4)` is a and 16y² is b

First, we need to find the two factors, when squared, equal
`9x^(4)` and 16y²

let's start with
`9x^(4)`

9 is 3 squared;
`x^(4)` is x² squared

let's try 3x² as a factor

To double check, we can square it

(3x²)²

apply the Laws of Exponents; square 3 and multiply the power by 2

when you solve, the answer will be
`9x^(4)`

So it works

now let's find the factor for 16y²

16 is 4 squared, and y² is y squared

so let's try 4y

(4y)²

apply the Laws of Exponents; square 4 and multiply the power by 2

the result is 16y²

Also works!

Now let's apply the formula; as said above,
`9x^(4)` is a and 16y² is b

so:
`9x^(4)`-16y²=(3x²+4y)(3x²-4y)

we can even double check this:

multiply the 2 binomials; apply FOIL

`9x^(4)`-12x²y+12x²y-16y²

the 2 12x²y's cancel out

and the result is

`9x^(4)`-16y²

Hope this helps!