Completely factor the following expression:100x2 – 160xy + 64y2
100x2 – 160xy + 64y2
=4(25x²-40xy+16y²)
=4((5x)²-2*5x*4y+(4y)²)
=...
use (a-b)²=a²-2ab+b²
to complete the factorization.
To completely factor the expression 100x^2 - 160xy + 64y^2, we need to find the factors of each term and look for a common factor that can be factored out.
Let's start by writing out the factors for each term:
100x^2: Since 100 is a perfect square, we can factor it as (10x)^2.
-160xy: The coefficient -160 can be factored as -2 * 2 * 2 * 2 * 5, and we can group the variables as x * y. So, we can write it as -2^4 * 5 * x * y = (-2^2 * 5xy)(2^2 * y) = (-20xy)(4y) = -20xy * 4y.
64y^2: Similar to 100x^2, 64 is a perfect square. We can factor it as (8y)^2.
Now let's rewrite the expression with the factored terms:
100x^2 - 160xy + 64y^2
= (10x)^2 - 20xy * 4y + (8y)^2
= (10x - 4y)(10x - 4y)
So, the completely factored expression is (10x - 4y)(10x - 4y).