Question

THIS IS AN ESSAY NOT JUST AN ANSWER

Prompt:
What does it mean to multiply polynomials?
Explain how to multiply (x + 2) (X - 4) as if you're teaching a student a year
younger than you.

Answer 1

We can simply use distributive law of grade 1

• (a+b)(c+d)=ac+ad+bc+bd

I assume you know multiplication of monomials

So

• (x+2)(x-4)
• x(x-4)+2(x-4)
• x²-4x+2x-8
• x²-2x-8

Answer 2

• We assume before this you have learned how to multiply two monomials and monomial with binomial.

Use the following formula to multiply binomials:

• (a + b)(c + d) = ab + ad + bc + bd

Applied to the given expression, we have:

• (x + 2)(x - 4), where a = x, b = 2, c = x , d = -4

Expand as indicated above:

• (x + 2)(x - 4) =
• x(x) + x(-4) + 2(x) + 2(-4)

Now simplify

• x² - 4x + 2x - 8

Collect like terms, (-4x) and (2x):

• x² + (-4x + 2x) - 8 =
• x² - 2x - 8

This is how you can do same order operations with any binomials.