Multiplication of Two Binomials Examples

What is (xy + y²)(2x + 9y)?

Distribute (xy + y²) over (2x + 9y) to find:

(xy + y²)(2x) + (xy + y²)(9y)

Distribute further to get:

(xy)(2x) + (y²)(2x) + (xy)(9y) + (y²)(9y)

And then simplify:

2x²y + 2xy² + 9xy² + 9y³ =
2x²y + 11xy² + 9y³

See? Ain't no thang.

Find the product: (4x² + 10x)(2x + 3).

Let's distribute it up:

(4x² + 10x)(2x + 3) =
(4x² + 10x)(2x) + (4x² + 10x)(3) =
(4x²)(2x) + (10x)(2x) + (4x²)(3) + (10x)(3)

Tame this beast by multiplying everything out:

8x³ + 20x² + 12x² + 30x

Then simplify:

8x³ + 32x² + 30x

What's the product of (2xy – y) and (3x² + 7xy)?

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

(2xy)(3x²) + (2xy)(7xy) + (-y)(3x²) + (-y)(7xy)

This simplifies to:

6x³y + 14x²y² – 3x²y – 7xy²