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Find the factors of $7x+14y+bx+2by$
in Mathematics by Diamond (74,874 points) | 48 views

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Find the factors of $7x+14y+bx+2by$

Step 1 - There are no factors common to all terms

Step 2 - Group terms with common factors together}$x$ is a common factor of the first and third terms and $2y$ is a common factor of the second and fourth terms $(7:b~=~14:2b)$.

Step 3 - Rearrange the equation with grouped terms together

\[ \begin{align*}
7x+14y+bx+2by &= (7x+bx)+(14y+2by) \\
&= x(7+b)+2y(7+b) \end{align*}\]

Step 4 - Take out the common factor $(7+b)$
 

\[ \begin{equation*}
x(7+b)+2y(7+b) = (7+b)(x+2y)
\end{equation*}\]


Step 5 - Write the final answer
The factors of $7x+14y+bx+2by$ are $(7+b)$ and $(x+2y)$.

by Diamond (43,672 points)
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