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Find (xy + y^{2})(2x + 9y).

Distribute (xy + y^{2}) over (2x + 9y) to find

(xy + y^{2})(2x) + (xy + y^{2})(9y)

Distribute further to get

(xy)(2x) + (y^{2})(2x) + (xy)(9y) + (y^{2})(9y)

and then simplify for

2x^{2}y + 2xy^{2} + 9xy^{2} + 9y^{3}

which can be combined further to give us

2x^{2}y + 11xy^{2} + 9y^{3}.

Find the product (4x^{2} + 10x)(2x + 3).

Let's FOIL it up.

The product of the first terms is

(4x^{2})(2x)=8x^{3}

The product of the outside terms is

(4x^{2})(3)=12x^{2}

The product of the inside terms is

(10x)(2x)=20x^{2}

The product of the last terms is

(10x)(3)=30x

Adding the little products yields

8x^{3} + 12x^{2} + 20x^{2} + 30x

which simplifies to

8x^{3} + 32x^{2} + 30x.

Find the product (2xy - y)(3x^{2} + 7xy).

Using FOIL, we find

(2xy)(3x^{2}) + (2xy)(7xy) + (-y)(3x^{2}) + (-y)(7xy)

This simplifies to

6x^{3}y + 14x^{2}y^{2} - 3x^{2}y - 7xy^{2}

Make it rain.