Упростите выражение(a+2b)² - (a+b) ( b+a) при а =1 и b = 1/5

Для упрощения данного выражения нужно сначала раскрыть скобки.

(a + 2b)² = a² + 4ab + 4b² (a + b)(b + a) = ab + a² + ab + b² = 2ab + a² + b²

Теперь подставим значения a = 1 и b = 1/5:

(a + 2b)² = 1² + 41(1/5) + 4(1/5)² = 1 + 4/5 + 4/25 = 1 + 0.8 + 0.16 = 1.96 (a + b)(b + a) = 21*(1/5) + 1² + (1/5)² = 2/5 + 1 + 1/25 = 0.4 + 1 + 0.04 = 1.44

Теперь вычтем второе выражение из первого:

1.96 - 1.44 = 0.52

Таким образом, упрощенное выражение (a + 2b)² - (a + b)(b + a) при а = 1 и b = 1/5 равно 0.52.

Упростим данное выражение при а = 1 и b = 1/5:

(a+2b)² - (a+b)(b+a) = (1+2*(1/5))² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)² - (1+1/5)(1/5+1) = (1+2/5)

Для того чтобы упростить выражение ((a+2b)² - (a+b)(b+a)) при (a = 1) и (b = \frac{1}{5}), сначала разложим выражение и упростим его в общем виде.

1. Раскроем скобки:

[ (a + 2b)^2 - (a + b)(b + a) ]

1. Используем формулу квадрата суммы для первой части:

[ (a + 2b)^2 = a^2 + 2 \cdot a \cdot 2b + (2b)^2 = a^2 + 4ab + 4b^2 ]

1. Перемножим скобки во второй части:

[ (a + b)(b + a) = a \cdot b + a \cdot a + b \cdot b + b \cdot a = ab + a^2 + b^2 + ab = a^2 + 2ab + b^2 ]

1. Теперь подставим полученные выражения обратно:

[ (a^2 + 4ab + 4b^2) - (a^2 + 2ab + b^2) ]

1. Сгруппируем подобные члены и упростим:

[ a^2 + 4ab + 4b^2 - a^2 - 2ab - b^2 = (a^2 - a^2) + (4ab - 2ab) + (4b^2 - b^2) ]

[ 0 + 2ab + 3b^2 = 2ab + 3b^2 ]

Теперь подставим значения (a = 1) и (b = \frac{1}{5}):

1. Подставим (a) и (b) в выражение:

[ 2(1) \left(\frac{1}{5}\right) + 3\left(\frac{1}{5}\right)^2 ]

1. Упростим:

[ 2 \cdot \frac{1}{5} + 3 \cdot \frac{1}{25} = \frac{2}{5} + \frac{3}{25} ]

1. Найдем общий знаменатель для сложения дробей:

[ \frac{2}{5} = \frac{2 \cdot 5}{5 \cdot 5} = \frac{10}{25} ]

[ \frac{10}{25} + \frac{3}{25} = \frac{10 + 3}{25} = \frac{13}{25} ]

Таким образом, упрощенное выражение при (a = 1) и (b = \frac{1}{5}) равно (\frac{13}{25}).