Multiply x² + 2x + 1 by x – 1.

It's Distribution O'Clock.

(x – 1)(x² + 2x + 1) =

x(x² + 2x + 1) – 1(x² + 2x + 1) =

x³ + 2x² + x – x² – 2x – 1

Variables refuse to go anywhere without their friends, so we'll gather the like terms together. We'll never make it to the movies in time otherwise.

x³ + (2x² – x²) + (x – 2x) – 1

x³ + x² – x – 1

If we hurry, we'll still catch the midnight showing of Weekend at Bernie's.

Multiply a – b – c by a + b + c.

(a – b – c )(a + b + c)

To multiply, you need steady hands, clear eyes, and nerves of math.

a(a + b + c) – b(a + b + c) – c(a + b + c) =

a² + ab + ac – ab – b² – bc – ac – bc – c²

We like like terms.

a² + (ab – ab) + (ac – ac) – b² + (-bc – bc) – c² =

a² – b² – 2bc – c²

Multiply 2m² + mn + 3n² by m² – 2mn + n².

(2m² + mn + 3n²)(m² – 2mn + n²)

Just take it slow, and make sure not to miss any terms.

2m²(m² – 2mn + n²) + mn(m² – 2mn + n²) + 3n²(m² – 2mn + n²) =

2m⁴ – 4m³n + 2m²n² + m³n – 2m²n² + mn³ + 3m²n² – 6mn³ + 3n⁴ =

2m⁴ + (-4m³n + m³n) + (2m²n² – 2m²n² + 3m²n²) + (mn³ – 6mn³) + 3n⁴

Here too. It's easy to skip over a number and not include it when collecting the like terms.

2m⁴ – 3m³n + 3m²n² – 5mn³ + 3n⁴

Multiply (2x – 5)(3x² + 7x – 1).

Go to town with the distributive property.

2x(3x² + 7x – 1) – 5(3x² + 7x – 1) =

6x³ + 14x² – 2x – 15x² – 35x + 5

Now collect the like terms and add them up.

6x³ + (14x² – 15x²) + (-2x – 35x) + 5 =

6x³ – x² – 37x + 5