Multiply

{x^2+x-6} * {x^3y}
_______ _________
{xy^2 } {x^2+6x+9}

x^2+x-6 = (x+3)(x-2)

x^2+6x+9 = (x+3)(x+3)
so we can cancel the (x+3) to get

(x-2)/(x+3) * x^2/y = x^2(x-2) / y(x+3)

thsnk you steve

To multiply the given expressions, we can use the distributive property multiple times. Here are the steps:

Step 1: Multiply the first term of the numerator ({x^2+x-6}) with the first term of the denominator ({x^3y}):
(x^2) * (x^3y) = x^(2+3) * y = x^5y

Step 2: Multiply the first term of the numerator ({x^2+x-6}) with the second term of the denominator ({x^2+6x+9}):
(x^2) * (x^2+6x+9) = x^2 * x^2 + x^2 * 6x + x^2 * 9 = x^(2+2) + 6x^(2+1) + 9x^2 = x^4 + 6x^3 + 9x^2

Step 3: Multiply the second term of the numerator ({x^2+x-6}) with the first term of the denominator ({xy^2}):
(x) * (xy^2) = x^(1+1) * y^2 = xy^2

Step 4: Multiply the second term of the numerator ({x^2+x-6}) with the second term of the denominator ({x^2+6x+9}):
(x) * (x^2+6x+9) = x * x^2 + x * 6x + x * 9 = x^(1+2) + 6x^(1+1) + 9x = x^3 + 6x^2 + 9x

Step 5: Multiply the third term of the numerator ({x^2+x-6}) with the first term of the denominator ({xy^2}):
(-6) * (xy^2) = -6xy^2

Step 6: Multiply the third term of the numerator ({x^2+x-6}) with the second term of the denominator ({x^2+6x+9}):
(-6) * (x^2+6x+9) = -6 * x^2 - 6 * 6x - 6 * 9 = -6x^2 - 36x - 54

Now we can write the final expression by combining the terms:

Final expression:
(x^5y + x^4 + 6x^3 + 9x^2 + xy^2 - 6xy^2) / (x^2 + 6x + 9)

Simplifying this expression further would involve grouping like terms and factorizing, but this is the expanded form of the multiplication.