```Question 115729
Do you want to factor?

{{{x^2(y^2+3y-4)}}} Factor out the GCF {{{x^2}}}

Now let's focus on the inner expression {{{y^2+3y-4}}}

Looking at {{{y^2+3y-4}}} we can see that the first term is {{{y^2}}} and the last term is {{{-4}}} where the coefficients are 1 and -4 respectively.

Now multiply the first coefficient 1 and the last coefficient -4 to get -4. Now what two numbers multiply to -4 and add to the  middle coefficient 3? Let's list all of the factors of -4:

Factors of -4:

1,2

-1,-2 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -4

(1)*(-4)

(-1)*(4)

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

Now which of these pairs add to 3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 3

<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">-4</td><td>1+(-4)=-3</td></tr><tr><td align="center">-1</td><td align="center">4</td><td>-1+4=3</td></tr></table>

From this list we can see that -1 and 4 add up to 3 and multiply to -4

Now looking at the expression {{{y^2+3y-4}}}, replace {{{3y}}} with {{{-1y+4y}}} (notice {{{-1y+4y}}} adds up to {{{3y}}}. So it is equivalent to {{{3y}}})

{{{y^2+highlight(-1y+4y)+-4}}}

Now let's factor {{{y^2-1y+4y-4}}} by grouping:

{{{(y^2-1y)+(4y-4)}}} Group like terms

{{{y(y-1)+4(y-1)}}} Factor out the GCF of {{{y}}} out of the first group. Factor out the GCF of {{{4}}} out of the second group

{{{(y+4)(y-1)}}} Since we have a common term of {{{y-1}}}, we can combine like terms

So {{{y^2-1y+4y-4}}} factors to {{{(y+4)(y-1)}}}

So this also means that {{{y^2+3y-4}}} factors to {{{(y+4)(y-1)}}} (since {{{y^2+3y-4}}} is equivalent to {{{y^2-1y+4y-4}}})

{{{x^2(y+4)(y-1)}}} Now reintroduce the GCF

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