Question

(2x +1)(x -6) Use the FOIL method of multiplying polynomials. Pls as u answer explain the method step by step !

Answer 1

FOIL (FIRST,OUTER,INSIDE,LAST):
FIRST: 2x * x
OUTER: 2x * (-6)
INSIDE: 1 * x
LAST: 1 * (-6)

Answer 2

and then add those together

Answer 3

first is 2x square
outer is -12x
inner is 1x
last is -6
am i right ? @Brandon77

Answer 4

yep you sure are

Answer 5

so the answer is just those terms added together

Answer 6

@Brandon77 okay, then how do we write the answer? what is the way to write?

Answer 7

2x^2-12x+x-6
simplifies to 2x^2-11x-6

Answer 8

if the equation has (a-b)(a-b) or (a+b)(a+b) then is it still the same method?

Answer 9

yes the signs may change a little

Answer 10

Yes it's always the same. But a better way to think of this "polynomial expansion" would be through what the distributive property tells us. Using FOIL confines us to just being able to expanding factored trinomials (trinomials are expressions with 3 terms), such as (a + b)(a + b) or something similar. What if we had (a + b)( a + b + c)? We would no longer be able to use FOIL. And this is where the distributive property plays a crucial role.

The distributive property essentially tells us to "distribute" terms something like this:

If I had (a + b)(a + b), then that means that a in the first bracket gets "distributed" or multiplied by every term in the other bracket. Similarly, the b in the first bracket also gets multiplied by every term in the other bracket. So we get:

(a + b)(a + b) = a(a + b) + b( a + b) = a^2 + ab + ba + b^2 = a^2 + 2ab + b^2

As you can see, the a gets multiplied by the other bracket, and the same happens with b and we can further multiply those out to get the answer. As a matter of fact, FOIL itself is derived from the use of distributive property which is why its so crucial to understand so you can expand something that looks like this:

(a + b)(a + b + c), we must again "distribute" a to every term in the next bracket and same goes for b.

(a + b)(a + b + c) = a(a + b + c) + b(a + b + c) = a^2 + ab + ac + ba + b^2 + bc
= a^2 + b^2 + 2ab + ac + bc

And now we will have no problem expanding any factored polynomial no matter how long it gets! You might also want to look at binomial expansion with pascal's triangle which is very cool and can be very helpful since at times, using the distributive property can get messy and lengthy, and the pascal's triangle provides a very easy way of finding the expansions of binomials in the form (a + b)^n, where n is any integer.

@tanya123

Answer 11

like the - will bcome + and the - will become + ?

Answer 12

Applying distributive property once again to (a - b)(a - b), we once again, "distribute" all the terms to each letter in the bracket:

(a - b)(a - b) = a(a - b) - b(a - b) <-- See how each letter in first bracket gets multiplied by all the terms in the next?

(a - b)(a - b) = a(a - b) - b(a - b) = a^2 -ab - ba + b^2 = a^2 - 2ab + b^2

Makes sense? Remember the sign btw, multiplying 2 negatives gives positive, negative/positive gives negative, and positive/positive obviously gives positive.

@tanya123

Answer 13

thank you soo much @genius12 that explain it!!!

Answer 14

and @Brandon77 u were excellent too thank you soo very much!!!! :)