Question

Factor x^3y^2 - x^5 + xy^3 - yx^3

Answer 1

Steps:

So firstly, we need to factor out the GCF. Since all the terms share a GCF of x, factor that out as such:

$(x)(x^2y^2-x^4+y^3-yx^2)$

Next, I will be factoring by grouping. For this, factor x²y² + y³ and -x⁴ - yx². Make sure that they have the same quantity on the inside:

$(x)(y^2(x^2+y)-x^2(x^2+y))$

Now rewrite the expression as:

$(x)(y^2-x^2)(x^2+y)$

However, we can factor this expression further. Next, we will be applying the difference of squares rule, which is $x^2-y^2=(x+y)(x-y)$ . In this case:

$y^2-x^2=(y+x)(y-x)\\\\(x)(y+x)(y-x)(x^2+y)$

Answer:

In short, the factored form of this expression is:

$(x)(y+x)(y-x)(x^2+y)$