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What is (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:

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

See? Ain't no thang.

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

Let's distribute it up:

(4x^{2} + 10x)(2x + 3) =(4x^{2} + 10x)(2x) + (4x^{2} + 10x)(3) =(4x^{2})(2x) + (10x)(2x) + (4x^{2})(3) + (10x)(3)

Tame this beast by multiplying everything out:

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

Then simplify:

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

What's the product of (2xy – y) and (3x^{2} + 7xy)?

After a couple rounds of distribution, we're at:

(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.

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