Question

Помагите пожалуста упростите выражение: 1) m² - 2mn + n² ...m - n --------------------- : ---------- <--- дробь m² - mn + n² ......m³ + n3 2) a² + b² - ab .........a³ + b³ ---------------------- : ------------------ x² - y² ...............x² + y² - 2xy

Answer 1

1) m² - 2mn + n²     m - n              (m-n)^2         (m+n)*(m^2-mn+n^2)    
--------------------- :   ---------- = -------------------  * ----------------------------- =  (m-n)*(m+n) =m^2-n^2
   m² - mn + n²       .m³ + n3   m^2-mn+n^2           m-n

2) a² + b² - ab           a³ + b³                a^2-ab+b^2               (x-y)^2                    x-y
---------------------- : ------------------ =   ------------------- *  ---------------------------- = ----------------
       x² - y²               x² + y² - 2xy          (x-y)*(x+y)           (a+b)*(a^2-ab+b^2)     (a+b)*(x+y)

Answer 2

Simplifying the Expressions

To simplify the given expressions, let's break them down step by step:

Expression 1: 1) m² - 2mn + n² ... m - n 2) m² - mn + mn - n² ... m - n (grouping like terms) 3) (m² - mn) + (mn - n²) ... m - n (rearranging terms) 4) m(m - n) + n(m - n) ... m - n (factoring out common terms) 5) (m + n)(m - n) ... m - n (simplifying further)

Therefore, the simplified form of the expression is (m + n)(m - n).

Expression 2: 1) a² + b² - ab ... a³ + b³ 2) a² + b² - ab + ab - a³ - b³ ... a³ + b³ (grouping like terms) 3) (a² - ab + ab) + (b² - a³ - b³) ... a³ + b³ (rearranging terms) 4) a(a - b) + b² - a³ - b³ ... a³ + b³ (factoring out common terms) 5) a(a - b) + b(b² - b²) - a³ - b³ ... a³ + b³ (factoring out common terms) 6) a(a - b) + b(b² - 1) - a³ - b³ ... a³ + b³ (simplifying further) 7) a(a - b) + b(b - 1)(b + 1) - a³ - b³ ... a³ + b³ (factoring out common terms)

Therefore, the simplified form of the expression is a(a - b) + b(b - 1)(b + 1) - a³ - b³.

Expression 3: 1) x² - y² ... x² + y² - 2xy 2) (x - y)(x + y) ... x² + y² - 2xy (simplifying further)

Therefore, the simplified form of the expression is (x - y)(x + y).

I hope this helps! Let me know if you have any further questions.