Binomial Distribution - (brack + et) (brac + ket)

What does FOIL stand for?

F - first

O - outer

I - inner

L - last

(x + 3)(x + 2)

• Step 1: FOIL

F: x × x = x²
O: x × 2 = 2x
I: 3 × x = 3x
L: 3 × 2 = 6

• Step 2: Combine like terms

x² + 2x + 3x + 6 =

x² + 5x + 6

• Final Answer:

x² + 5x + 6

When multiplying two binomials which only differ only in sign:

• Square the first and last term and separate them with a minus sign

  • (a + b) (a - b) = a² - b²

(x - 3)(x + 3)

• Step 1: FOIL

F: x × x = x²
O: x × 3 = 3x
I: -3 × x = -3x
L: -3 × 3 = -9

• Step 2: Combine like terms

x² + 3x - 3x - 9 =

x² - 9

• Final Answer:

x² - 9

When a binomial is squared:

• Square the first term

• Multiply the two expressions inside the brackets and the multiply by two

• Square the last term which will always be positive

  • (a + b)² = a² +2ab + b²

(x + 4)² = (x + 4)(x + 4)

• Step 1: FOIL

F: x × x = x²
O: x × 4 = 4x
I: 4 × x = 4x
L: 4 × 4 = 16

• Step 2: Combine like terms

x² + 4x + 4x + 16 =

x² + 8x + 16

• Final Answer:

x² + 8x + 16