Решебник по алгебре 7 класс Мерзляк ФГОС Задание 735

 

\[\boxed{\text{735\ (735).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ x² - 4x + 3 =\]

\[= \left( x^{2} - 4x + 4 \right) - 1 =\]

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

\[= (x - 2 - 1)(x - 2 + 1) =\]

\[= (x - 3)(x - 1)\]

\[2)\ a² + 2a - 24 =\]

\[= \left( a^{2} + 2a + 1 \right) - 25 =\]

\[= (a + 1)^{2} - 25 =\]

\[= (a + 1 - 5)(a + 1 + 5) =\]

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

\[3)\ y² + 12y + 35 =\]

\[= \left( y^{2} + 12y + 36 \right) - 1 =\]

\[= (y + 6)^{2} - 1 =\]

\[= (y + 6 - 1)(y + 6 + 1) =\]

\[= (y + 5)(y + 7)\]

\[4)\ x² + x - 6 =\]

\[= \left( x^{2} + x + \frac{1}{4} \right) - 6,25 =\]

\[= (x + 0,5)^{2} - 2,5² =\]

\[= (x + 0,5 + 2,5)(x + 0,5 - 2,5) =\]

\[= (x + 3)(x - 2)\]

\[5)\ c² + 8cd + 15d² =\]

\[= \left( c^{2} + 8cd + 16d^{2} \right) - d^{2} =\]

\[= (c + 4d)^{2} - d^{2} =\]

\[= (c + 4d - d)(c + 4d + d) =\]

\[= (c + 3d)(c + 5d)\]

\[6)\ 9x² - 30xy + 16y^{2} =\]

\[= \left( 9x^{2} - 30xy + 25y^{2} \right) - 9y^{2} =\]

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

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

\[= (3x - 2y)(3x - 8y)\]

\[\boxed{\text{735.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ (a - b - c)(a + b - c) =\]

\[= \left( (a - c) - b \right)\left( (a - c) + b \right) =\]

\[= (a - c)^{2} - b^{2} =\]

\[= a^{2} - 2\text{ac} + c^{2} - b^{2}\]

\[2)\ (a - b + c + d)(a - b - c - d) =\]

\[{= (a - b)² - (c + d)^{2} = }{= a² - 2ab + b^{2} - c^{2} - 2cd - d²}\]