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### Course: Algebra (all content)>Unit 10

Lesson 8: Multiplying binomials by polynomials

# Multiplying binomials by polynomials challenge

Sal finds the values of coefficients a and b that make (2x+4)(5x-9)=ax²+bx-46 true for all x-values.

## Want to join the conversation?

• Why can't we just use a calculator?
• Because you have to burn your brain cells and pass the test.
• If the trinomial is in the front and the binomial comes afte, do you FOIL the binomial into the trinomial or do you FOIL the trinomial into the binomial?
• It doesn't matter. The commutative property of multiplication applies.
Remember: 2*3 is the same as 3*2.
This same concept applies when you multiply polynomials.
Hope this helps.
• At what was all about the constant terms
• The constant terms are the ones that don't have any variables. If you do something we call the "Box method", they are the ones you should get in the bottom right. Again, they don't have a variable. No letter A-Z. I hope this helps you out!
• when multiplying polynomials and simplifying it. do i add the exponents -2mn(m2-4m-7n2) = -2m3n+8m2n+14mn2
• Yes, the properties of exponents tell us to add exponents when we are multiplying items with a common base.
FYI... write exponents correctly. you should have: -2m^3n+8m^2n+14mn^2
Without the symbols for exponents, you have -2m * 3n = -6mn
• What is the box method? Is it the same as FOIL?
(1 vote)
• - There is no way to get the a and b values, except for a leap of logical faith and proving it afterwards?

I was trying to solve for a or b, but without a second equation, it seems impossibru.
(1 vote)
• In the video it shows (2x+4)(5x-9)
I'll do that equation.
you do foil(first, outer, inner last)
the layout is this: (dx + a) (cx + b)
(dx * cx) (first) + (dx*b) (outer) + (a*cx) (inner) + (a*b) last.
So you get (2x * 5x) (first) + (2x*-9) (outer) + (4*5x) (inner) + (4*-9) last.
You then get 10x^2 + -18x + 20x + -36
Which simplifies to 10x^2 + 2x - 36.
does this help?