25xsquare-40xy+16y square

21x. 17y

What is the answer

25x^2-40xy+16y^2 = ( 5 x - 4 y)^2

because:

( a - b )^2 = a^2 - 2 • a •b + b^2

25x^2-40xy+16y^2=5^2-2•5•4y+(4y)^2 = (5x-4y)^2

The given expression is 25x^2 - 40xy + 16y^2.

This expression is a quadratic expression in terms of x and y. To simplify it, we can look for common factors, if any, and then try to factorize it further.

First, let's see if there are any common factors among the terms. In this case, there are no common factors.

Next, let's try to factorize the expression. We can use the following formula to factorize quadratic expressions of the form ax^2 + bx + c:

(x - p)(x - q), where p and q are the roots of the equation ax^2 + bx + c = 0.

In this case, the expression is 25x^2 - 40xy + 16y^2.

To factorize it further, we need to find two numbers whose product is 25 times 16 (400) and whose sum is -40.

The numbers that satisfy these conditions are -20 and -20.

So, we can factorize the given expression as:

25x^2 - 40xy + 16y^2 = (5x - 4y)(5x - 4y)

This can also be written as:

(5x - 4y)^2

So, the simplified expression is (5x - 4y)^2.