Answer:
[tex]-4x^5y^3-3x^4y^3+x^5y^2[/tex]
Step-by-step explanation:
You need to know this indice rule:
If you multiply two terms with the same base, then add their powers and multiply their coefficients.
[tex](4x^2y+3xy-x^2)(-x^3y^2)[/tex] : Here we have to multiply each term in the first pair of brackets by the term in the second pair of brackets.
So we can split this into parts:
[tex](4x^2y)(-x^3y^2) +(3xy)(-x^3y^2)+(-x^2)(-x^3y^2)[/tex]
Now using the rule above expand the brackets:
[tex](4x^2y)(-x^3y^2) = -4x^5y^3[/tex] : Notice how [tex]y * y^2 =y^3[/tex] since [tex]y[/tex] [tex]= y^1[/tex] so [tex]1 + 2 = 3[/tex].
[tex](3xy)(-x^3y^2) = -3x^4y^3[/tex]
[tex](-x^2)(-x^3y^2)[/tex] [tex]= x^5y^2[/tex] : Be careful with negatives, two negatives make a positive.
Now add them all together:
[tex]-4x^5y^3-3x^4y^3+x^5y^2[/tex]
