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

(3x²+4y)(3x²-4y)

Step-by-step explanation:

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

So we need to apply that formula to -16y², where is a and 16y² is b

First, we need to find the two factors, when squared, equal and 16y²

let's start with

9 is 3 squared; 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

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, is a and 16y² is b

so: -16y²=(3x²+4y)(3x²-4y)

we can even double check this:

multiply the 2 binomials; apply FOIL

-12x²y+12x²y-16y²

the 2 12x²y's cancel out

and the result is

-16y²

Hope this helps!

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step-by-step explanation: