```Question 251213

Looking at {{{x^2-6xy-40y^2}}} we can see that the first term is {{{x^2}}} and the last term is {{{-40y^2}}} where the coefficients are 1 and -40 respectively.

Now multiply the first coefficient 1 and the last coefficient -40 to get -40. Now what two numbers multiply to -40 and add to the  middle coefficient -6? Let's list all of the factors of -40:

Factors of -40:

1,2,4,5,8,10,20,40

-1,-2,-4,-5,-8,-10,-20,-40 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -40

(1)*(-40)

(2)*(-20)

(4)*(-10)

(5)*(-8)

(-1)*(40)

(-2)*(20)

(-4)*(10)

(-5)*(8)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to -6? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -6

<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">-40</td><td>1+(-40)=-39</td></tr><tr><td align="center">2</td><td align="center">-20</td><td>2+(-20)=-18</td></tr><tr><td align="center">4</td><td align="center">-10</td><td>4+(-10)=-6</td></tr><tr><td align="center">5</td><td align="center">-8</td><td>5+(-8)=-3</td></tr><tr><td align="center">-1</td><td align="center">40</td><td>-1+40=39</td></tr><tr><td align="center">-2</td><td align="center">20</td><td>-2+20=18</td></tr><tr><td align="center">-4</td><td align="center">10</td><td>-4+10=6</td></tr><tr><td align="center">-5</td><td align="center">8</td><td>-5+8=3</td></tr></table>

From this list we can see that 4 and -10 add up to -6 and multiply to -40

Now looking at the expression {{{x^2-6xy-40y^2}}}, replace {{{-6xy}}} with {{{4xy-10xy}}} (notice {{{4xy-10xy}}} combines back to {{{-6xy}}}. So it is equivalent to {{{-6xy}}})

{{{x^2+highlight(4xy-10xy)-40y^2}}}

Now let's factor {{{x^2+4xy-10xy-40y^2}}} by grouping:

{{{(x^2+4xy)+(-10xy-40y^2)}}} Group like terms

{{{x(x+4y)-10y(x+4y)}}} Factor out the GCF of {{{x}}} out of the first group. Factor out the GCF of {{{-10y}}} out of the second group

{{{(x-10y)(x+4y)}}} Since we have a common term of {{{x+4y}}}, we can combine like terms

So {{{x^2+4xy-10xy-40y^2}}} factors to {{{(x-10y)(x+4y)}}}

So this also means that {{{x^2-6xy-40y^2}}} factors to {{{(x-10y)(x+4y)}}} (since {{{x^2-6xy-40y^2}}} is equivalent to {{{x^2+4xy-10xy-40y^2}}})

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