Question

Factor. ​ 9x2−30xy+25y2 ​

Answer 1

Answer:

The factor form is: $\quad \left(3x-5y\right)^2$

Step-by-step explanation:

When the factor of the expression is required to be found, then take the common terms, or can be done by using the standard formulas, for example, $\left(a-b\right)^2=a^2-2ab+b^2$

Now, here we have to find the factor of the expression:

$9x^2-30xy+25y^2\\=\left(3x\right)^2-2\cdot \:3x\cdot \:5y+\left(5y\right)^2$

So now, we can see that this is the perfect square form of:

$\left(a-b\right)^2=a^2-2ab+b^2$

So the given expression is factorized as follows:

$\left(3x\right)^2-2\cdot \:3x\cdot \:5y+\left(5y\right)^2=\left(3x-5y\right)^2$

Thus the factored form is:

$9x^2-30xy+25y^2 = \quad \left(3x-5y\right)^2$