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Đáp án + Giải thích các bước giải:

Bài $\textbf{5}.$

$\textbf{1}\bigg)$

$\begin{array}{l} & 2y(x + 2) - 3x - 6
\\ &= 2y(x + 2) - (3x + 6)
\\ &= 2y(x + 2) - 3(x + 2)
\\ &= (2y - 3)(x + 2)\end{array}$

$\textbf{2}\bigg)$

$\begin{array}{l} & 3(x + 4) - x^2 - 4x
\\ &= 3(x + 4) - (x^2 + 4x)
\\ &= 3(x + 4) - x(x + 4)
\\ &= (3 - x)(x + 4)\end{array}$

$\textbf{3}\bigg)$

$\begin{array}{l} & 2(x + 5) - x^2 - 5x
\\ &= 2(x + 5) - (x^2 + 5x)
\\ &= 2(x + 5) - x(x + 5)
\\ &= (2 - x)(x + 5) \end{array}$

$\textbf{4}\bigg)$

$\begin{array}{l} & x^2 + 6x - 3(x + 6)
\\ &= x(x + 6) - 3(x + 6)
\\ &= (x - 3)(x + 6) \end{array}$

$\textbf{5}\bigg)$

$\begin{array}{l} & x(x + y) - 5x - 5y
\\ &= x(x + y) - (5x + 5y)
\\ &= x(x + y) - 5(x + y)
\\ &= (x - 5)(x + y) \end{array}$

$\textbf{6}\bigg)$

$\begin{array}{l} & x(x - y) + 2x - 2y
\\ &= x(x - y) + 2(x - y)
\\ &= (x + 2)(x - y) \end{array}$

$\textbf{7}\bigg)$

$\begin{array}{l} & 2x - 6 + 5x(x - 3)
\\ &= 2(x - 3) + 5x(x - 3)
\\ &= (5x + 2)(x -3 ) \end{array}$

$\textbf{8}\bigg)$

$\begin{array}{l} & 3x(x - 2) - 4x + 8
\\ &= 3x(x - 2) - (4x - 8)
\\ &= 3x(x - 2) - 4(x - 2)
\\ &= (3x - 4)(x - 2)\end{array}$

$\textbf{9}\bigg)$

$\begin{array}{l} & x(x + y) - 3x - 3y
\\ &= x(x + y) - (3x + 3y)
\\ &= x(x + y) - 3(x + y)
\\ &= (x - 3)(x + y)\end{array}$

$\textbf{10}\bigg)$

$\begin{array}{l} & x(x + y) - 7x - 7y
\\ &= x(x + y) - (7x + 7y)
\\ &= x(x + y) - 7(x + y)
\\ &= (x - 7)(x + y)\end{array}$

$\textbf{11}\bigg)$

$\begin{array}{l} & x^2(x - y) + 2x - 2y
\\ &= x^2(x - y) + 2(x - y)
\\ &= (x^2 + 2)(x - y)\end{array}$

$\textbf{12}\bigg)$

$\begin{array}{l} & x(x +3y) - 5x - 15y
\\ &= x(x + 3y) - (5x + 15y)
\\ &= x(x + 3y) - 5(x + 3y)
\\ &= (x - 5)(x + 3y)\end{array}$