ГДЗ по алгебре 7 класс Макарычев Задание 797

\[\boxed{\text{797\ (797).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[(10a + b)(10a + c) =\]

\[= 100a(a + 1) + bc\]

\[100a^{2} + 10ac + 10ab + bc =\]

\[= 100a(a + 1) + bc\]

\[100a^{2} + 10a \cdot (b + c) + bc =\]

\[= 100a(a + 1) + bc\]

\[100a^{2} + 10a \cdot 10 + bc =\]

\[= 100a(a + 1) + bc\]

\[100a(a + 1) + bc =\]

\[= 100a(a + 1) + bc\]

\[\Longrightarrow верно.\]

\[\textbf{а)}\ 23 \cdot 27 =\]

\[= (2 \cdot 10 + 3)(2 \cdot 10 + 7) =\]

\[= 100 \cdot 2 \cdot (2 + 1) + 3 \cdot 7 =\]

\[= 200 \cdot 3 + 21 = 621\]

\[\textbf{б)}\ 42 \cdot 48 =\]

\[= (4 \cdot 10 + 2)(4 \cdot 10 + 8) =\]

\[= 100 \cdot 4 \cdot (4 + 1) + 2 \cdot 8 =\]

\[= 400 \cdot 5 + 16 = 2000 + 16 =\]

\[= 2016\]

\[\textbf{в)}\ 59 \cdot 51 =\]

\[= (5 \cdot 10 + 9)(5 \cdot 10 + 1) =\]

\[= 100 \cdot 5 \cdot (5 + 1) + 9 \cdot 1 =\]

\[= 500 \cdot 6 + 9 = 3000 + 9 =\]

\[= 3009\]

\[\textbf{г)}\ 84 \cdot 86 =\]

\[= (8 \cdot 10 + 4)(8 \cdot 10 + 6) =\]

\[= 100 \cdot 8 \cdot (8 + 1) + 6 \cdot 4 =\]

\[= 800 \cdot 9 + 24 = 7200 + 24 =\]

\[= 7224\]