Question

factorize the following
9x^2-24xy+16y^2

help again please please ​

Answer 1

Answer:

(3x - 4y) (3x - 4y)

Step-by-step explanation:

[ Using Formula ]

Given:

$\sf \implies 9x^2-24xy+16y^2$

To Find:

Factorized form

Formula Used:

$\bf (x-y)^2 = x^2 - 2xy +y^2$

Procedure:-

We know that:-

Simplifying the expression values:-

$\implies \sf (3x)^2-3x.4y+(4y)^2$

According to the formula :-

$\bf (x-y)^2 = x^2 - 2xy +y^2$

So here we can infer that:-

x = 3 , y = 4

So, factorized form would be :-

$\implies{\boxed{ {\bf (3x -4y) (3x-4y)}}}$

Note down:-

• Factorisation is a method to find factors of the given polynomial.

• They are generally written as product of other factors.

• To factories a quadratic polynomial splitting the middle term is widely used.

• While identities, and simplification can also be used to factories.

• To factorize a quadratic equation splitting the middle term is much preferred.

• We search for a set of number which will add together to middle term. And also the same set of number should give a product as the last term.

• If p(a) = 0, p(b) = 0, then 'a,' and 'b' are factors. Now, you need to find what all possible values'a' and 'b' could take where constant term = a.b (375000 in this question.)

Answer 2

Question= factorize the following

9x^2-24xy+16y^2

Answer⬇️

Ok, for something like that, it’s not too hard.

For a typical quadratic equation you have

aX2+bX+c

But, in this case you have something slightly different.

what you have is an equation such that you want to split it up into

(aX+bY)(cX+dY)

I’m ignoring the fact that this does come out to be a perfect square here, since YOU don’t know it.

Now, you have certain conditions for it, namely the coefficients;

a∗c=9

b∗d=16

a∗d+b∗c=24

Now, you’d normally need to fiddle around with those a bit — but notice that 9 and 16 are both Perfect Squares

32=9;42=16

Now, was this nice enough that the third equation works with 3 and 4? Well, a little math

3∗4=12;12+12=24

Yes! It does.

This means that

9x2+24xy+16y2=(3x+4y)2

Now, I have to assume that you typed in the question incorrectly - because there is not a ready and easy way to factor it if it is -16 rather than +16, at least not with the +24xy in the middle, because

(3x+4y)(3x−4y)=9x2−16y2

And you would still be left with the 24xy outside of the factored equation.

If you did type it up correctly, than Douglas Magowan has it right in that it’s Messy.