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    Factorising: Common factor

    \( \begingroup \)

    Question 1


    a)

    The expression $\var{pmult*pxcoeff}x+\var{pconstant*pmult}$ is a sum and can be factorised (written as a product) by finding the largest common factor:

     $\var{pmult*pxcoeff}x+\var{pconstant*pmult} = $  $\large($ interpreted as $\large)$

    We put the common factor out the front of a set of brackets and put the 'left-overs' inside.

    The (largest) common factor of  $\var{pmult*pxcoeff}x+\var{pconstant*pmult}$ is $\var{pmult}$. Once we remove that factor from each term in $\var{pmult*pxcoeff}x+\var{pconstant*pmult}$ we are left with $\var{pxcoeff}x+\var{pconstant}$.

    That means $\var{pmult*pxcoeff}x+\var{pconstant*pmult}= \var{pmult}(\var{pxcoeff}x+\var{pconstant})$.

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            b)

            Factorise $\simplify{{bp1}a+{bp2}}$

              $\large($ interpreted as $\large)$

            We put the common factor out the front of a set of brackets and put the 'left-overs' inside.

            The (largest) common factor of $\simplify{{bp1}a+{bp2}}$ is $\var{cf}$. Once we remove that factor from each term in $\simplify{{bp1}a+{bp2}}$ we are left with $\var{bx}a+\var{bc}$.

            That means $\simplify{{bp1}a+{bp2}}$ is $\var{cf} = \var{cf}(\var{bx}a+\var{bc})$.

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                    c)

                    Factorise $\simplify{{ct1}x+{ct2}y+{ct3}}$

                      $\large($ interpreted as $\large)$

                    We put the common factor out the front of a set of brackets and put the 'left-overs' inside.

                    The (largest) common factor of $\simplify{{ct1}x+{ct2}y+{ct3}}$ is $\var{cmult}$. Once we remove that factor from each term in $\simplify{{ct1}x+{ct2}y+{ct3}}$ we are left with $\simplify{{cx}x+{cy}y+{cc}}$.

                    That means $\simplify{{ct1}x+{ct2}y+{ct3}} = \simplify{{cmult}({ct1}x+{ct2}y+{ct3})}$.

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