Решебник по алгебре 7 класс Мерзляк Задание 500

\[\boxed{\text{500\ (500).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ (m - n) \cdot (m + n) = m^{2} - n^{2}.\]

\[2)\ (x - 1) \cdot (x + 1) = x^{2} - 1.\]

\[3)\ (9 - y) \cdot (9 + y) = 81 - y^{2}.\]

\[4)\ (3b - 1) \cdot (3b + 1) =\]

\[= (3b)^{2} - 1^{2} = 9b^{2} - 1.\]

\[5)\ (10m - 7) \cdot (10m + 7) =\]

\[= (10m)^{2} - 7^{2} = 100m^{2} - 49.\]

\[6)\ (4a - b) \cdot (b + 4a) =\]

\[= (4a)^{2} - b^{2} = 16a^{2} - b^{2}.\]

\[7)\ (5b + 1) \cdot (1 - 5b) =\]

\[= 1^{2} - (5b)^{2} = 1 - 25b^{2}.\]

\[8)\ (3x - 5y) \cdot (3x + 5y) =\]

\[= (3x)^{2} - (5y)^{2} = 9x^{2} - 25y^{2}.\]

\[9)\ (13c - 10d) \cdot (13c + 10d) =\]

\[= (13c)^{2} - (10d)^{2} =\]

\[= 169c^{2} - 100d^{2}.\]

\[10)\ (8m + 11n) \cdot (11n - 8m) =\]

\[= (11n)^{2} - (8m)^{2} =\]

\[= 121n^{2} - 64m^{2}\text{.\ }\]