Question

(а+5в)*(2а-в)-(а-2в)*(5а+в)

Answer 1

( а + 5в ) * ( 2а - в ) - ( а - 2в ) * ( 5а + в ) = 2а² - ав + 10ав - 5в² - ( 5а² + ав - 10ав + 2ав = 2а² - ав + 10ав - 5в² - 5а² - ав + 10ав - 2ав = -3а² + 19ав - 5в².

Удачи))

Answer 2

To simplify the expression (а+5в)(2а-в) - (а-2в)(5а+в), you need to perform the following steps:

Step 1: Distribute the terms within each set of parentheses.

First set of parentheses: (а + 5в) * (2а - в) = а * 2а + а * (-в) + 5в * 2а + 5в * (-в) = 2а^2 - ав + 10ав - 5в^2

Second set of parentheses: (а - 2в) * (5а + в) = а * 5а + а * в - 2в * 5а - 2в * в = 5а^2 + ав - 10ав - 2в^2

Step 2: Now, substitute the results back into the original expression.

Original expression: (а + 5в) * (2а - в) - (а - 2в) * (5а + в) = (2а^2 - ав + 10ав - 5в^2) - (5а^2 + ав - 10ав - 2в^2)

Step 3: Combine like terms.

= 2а^2 - ав + 10ав - 5в^2 - 5а^2 - ав + 10ав + 2в^2

Step 4: Simplify further.

Combine the terms with similar variables:

= (2а^2 - 5а^2) + (-ав - ав + 10ав) + (10ав) + (-5в^2 + 2в^2)

= -3а^2 + 9ав - 3в^2

So, the simplified expression is -3а^2 + 9ав - 3в^2.