Question

Multiply.
(2u-6x)(4u-3x+2)

Answer 1

Multiply the first term of (2u-6x) by each term in (4u-3x+2). Then multiply the second term of (2u-6x) by each term in (4u-3x+2). Add up all the pieces and simplify by collecting like terms.

In general, you multiply each term of each multiplier by each term of the other.

\[(a+b+c)(d+e+f) = a(d+e+f) + b(d+e+f) + c(d+e+f) = \]\[ad + ae + af + bd + be + bf + cd + ce + cf\]

Answer 2

so like.... 2u(4u-3x+2) - 6x(4u-3x+2)

Answer 3

Exactly. Now expand those two products, and you get?

Answer 4

so its 12u^2-30ux+18x-12

Answer 5

Not quite.

\[2u(4u-3x+2) = 2*4*u*u-2*3*u*x+2*2*u = 8u^2-6ux+4u\]
\[-6x(4u-3x+2) = -6*4*x*u -6(-3)*x*x -6*2*x = -24ux + 18x^2 -12x\]
Adding them together, \[8u^2-6ux+4u-24ux+18x^2-12x = \]

Answer 6

so, then I add like terms

Answer 7

Yes.

Answer 8

Ok! thanks for your help

Answer 9

What do you get for your result? you can just tell me which terms combine and what they combine to...

Answer 10

I got 12u^3-30ux^2+18^2-12x

Answer 11

How did you get a u^3 term?

Answer 12

8u squared and 4u

Answer 13

Look at my unsimplified result:
\[8u^2-6ux+4u-24ux+18x^2-12x\]The only two terms which can be combined are -6ux and -24ux.

You can't add 8u^2 + 4u like that.

Answer 14

You can only add them together if they have the same base and exponent.

Answer 15

8u + 4u = 12u
8u^2 + 4u^2 = 12u^2
8u^2 + 4u = 8u^2 + 4u (or you could write it as 4u(2u+1))

Answer 16

oh, i thought they were like terms as long as they had the same variable

Answer 17

As an example, suppose u = 3
8u^2 = 8*3*3 = 72
4u = 4*3 = 12
8u^2 + 4u = 72 + 12 = 84

However, with the statement that 8u^2 + 4u = 12u^3, you are saying that
72 + 12 = 12*3*3*3 = 108

Answer 18

Nope, have to have both the same base and the same exponent.

Answer 19

ok

Answer 20

With that in mind, what is your new, improved answer?

Answer 21

8u^2-30ux^2+4u+18x^2-12x

Answer 22

Now where did you get -30ux^2 from? Details are very important in algebra...

Answer 23

-6ux and -24ux

Answer 24

Add them together and the exponents do not change. -6ux -24ux = -30ux.

Answer 25

so its just -30ux

Answer 26

Yes. Final answer is \[8u^2-30ux+4u+18x^2-12x\]

Answer 27

that was really long

Answer 28

If we knew a value in place of x or u, it would collapse down to something smaller. But we don't...

Answer 29

ok. do you mind helping me with another problem?

Answer 30

Post it as another problem, I have to leave...

Answer 31

ok. cool