Question

(х-4у)²+4у(2х-4у) при х= - \frac{3}{5}

Answer 1

Решение
(х - 4у)² + 4у(2х - 4у) =
= x² - 8xy + 16y² + 8xy - 16y² = x²
x² = (- 3/5)² = 9/25

Answer 2

To evaluate the expression (х-4у)² + 4у(2х-4у) when x = -3/5, we substitute the value of x into the expression:

((-3/5) - 4y)² + 4y(2(-3/5) - 4y)

Let's simplify it step by step:

First, let's simplify the terms inside the parentheses:

(-3/5 - 4y)² = (-3/5 - 4y) * (-3/5 - 4y) = (9/25 + 12y/5 + 12y/5 + 16y²) = 9/25 + 24y/5 + 16y² = (9 + 120y + 400y²)/25 = (400y² + 120y + 9)/25

Next, let's simplify the other term:

4y(2(-3/5) - 4y) = 4y(-6/5 - 4y) = -24y/5 - 16y²

Now, let's substitute these simplified expressions back into the original expression:

(х-4у)² + 4у(2х-4у) = (400y² + 120y + 9)/25 + (-24y/5 - 16y²)

To further simplify, let's find a common denominator for the fractions:

(400y² + 120y + 9)/25 + (-24y/5 - 16y²) = (400y² + 120y + 9 - 24y - 80y²)/25 = (320y² + 96y + 9 - 24y)/25 = (320y² + 72y + 9)/25

Therefore, when x = -3/5, the expression (х-4у)² + 4у(2х-4у) simplifies to (320y² + 72y + 9)/25.