Question

(x+4y)²- 16y² factories the following by splitting the middle term or by using identity ​

Answer 1

$\maltese\LARGE\textsf{\underline{ SoLuTioN :-}}$

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{( x + 4y )² - ( 16y )²}$

$\large\textsf{ }$

⇝ By using the formula:-

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf\textcolor{purple}{a² - b² = ( a + b )( a - b )}}$

$\large\textsf{ }$

Here :-

• a = x + 4y
• b = 16y

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{[ ( x + 4y ) + ( 16y ) ] × [(x + 4y ) - ( 16y ) ]}$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf\textcolor{red}{( x + 20y )( x - 12y )}}$

$\large\textsf{ }$

Algebraic Formulas :-

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{( a + b )² = a² + b² + 2ab}$

$\qquad\tt{:}\longrightarrow\large\textsf{( a - b )² = a² + b² - 2ab}$

$\qquad\tt{:}\longrightarrow\large\textsf{a² - b² = ( a + b ) ( a - b )}$

$\qquad\tt{:}\longrightarrow\large\textsf{a² + b² = ( a + b )² - 2ab}$

$\qquad\tt{:}\longrightarrow\large\textsf{a³ + b³ = ( a + b ) ( a² - 2ab + b² )}$

$\qquad\tt{:}\longrightarrow\large\textsf{a³ - b³ = ( a - b ) ( a² + ab + b² )}$

$\qquad\tt{:}\longrightarrow\large\textsf{( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ac }$