Question

Imagine your younger relative—of middle school age—was taking an algebra course and asked for your help. How would you teach the multiplication of polynomials to her?

Answer 1

Can you give some examples of the polynomials he/she will face?

Answer 2

Distributive property.

Answer 3

i would start by multiplying
\(12\times 23\) and then replace \(10\) by \(x\) and multiply \((x+2)(2x+3)\)

Answer 4

2x2 + 3x - 5

2x2y2 + 3xy - 5xy2

5x + 3y +6x +2y

Answer 5

@gartncryst There aren't any multiplication involved in these expressions... You want the factorized form of these equations, like (x - 1)(2x+5) (which is equal to 2x^2 + 3x - 5)

Answer 6

I am looking for the wording of how to explain to a teen how to solve the problem

Answer 7

Distribute each term of the first polynomial to each term of the other polynomial.

Answer 8

So these are solutions, or you want them to turn 2x^2 + 3x - 5 to (x - 1)(2x+5)? This process is factorization, while the reverse of it is expansion (i.e polynomial multiplication)

But if you're just looking for explanations, remind them of the distributive property (as @CliffSedge has mentioned). A quick reminder from numbers first, then add in variables. Also, make sure they are taught the idea of indices.

Answer 9

If it's just multiplication of polynomials, then take two polynomials
a + b + c, and d + e + f
and demonstrate the distributive property.
(a + b + c)(d + e + f) = ad + ae +af +bd + be + bf + cd + ce +cf.
Remind about the law of sameness and combining like terms, and that should be all that is necessary.

Following satellite's and tyteen's suggestions as well of starting with whole numbers and working up to the generality with algebraic expressions.

Answer 10

use the box multiplication aka FOIL but the box is more powerful