Find the square root of 25xsquared-40xy+16ysquared
(a - b)^2 = a^2 - 2ab + b^2
vs
25x^2 - 40xy + 16y^2
what do you think?
To find the square root of the expression 25x^2 - 40xy + 16y^2, we can use the concepts of factoring and the square root property. Let's break it down step by step:
1. Start by factoring the expression as much as possible. We have:
25x^2 - 40xy + 16y^2
This expression can be factored into:
(5x - 4y)^2
2. Now, we can apply the square root property. Take the square root of both sides of the equation:
√[(5x - 4y)^2] = √[25x^2 - 40xy + 16y^2]
Remember that when taking the square root of a squared expression, you get the absolute value of the expression. So, we have:
|5x - 4y| = √[25x^2 - 40xy + 16y^2]
3. Finally, simplify the square root of the expression:
|5x - 4y| = √[(5x - 4y)^2]
Since we have the absolute value on the left side, we can remove it by considering both positive and negative solutions:
5x - 4y = ±√[(5x - 4y)^2]
So, the square root of 25x^2 - 40xy + 16y^2 is ±(5x - 4y).