Question

Find the product and enter it in the box below. Enter your answer as a polynomial in descending order and use the caret (^) for exponents. For example, you would write as 4x^2.

(2x2 + 10)(5 - x2)

Answer 1

Do you know how to start this?

Answer 2

no not at all

Answer 3

Are you familiar with the FOIL method?

Answer 4

no

Answer 5

Here is what FOIL stands for:
F - multiply the first terms of the binomials
O - multiply the outside terms of the binomials
I - multiply the inside terms of the binomials
L - multiply the last terms of the binomials

Answer 6

So we have \(\sf (2x^2~+~10)(5~-~x^2)\) right?

Answer 7

yes

Answer 8

Ok so the first part of the FOIL method is multiply the first terms. The first terms of the 2 binomials are \(\sf 2x^2\) and \(\sf 5\)

Answer 9

10^2 ?

Answer 10

Close, \(\sf 10x^2\)

Answer 11

What do you think the outside terms will be?

Answer 12

ok

Answer 13

next?

Answer 14

What do you think the outside terms will be?

Answer 15

wat i do to find it

Answer 16

The outside terms are going to be \(\sf 2x^2\) and \(\sf x^2\). What does that equal when they are mutliplied?

Answer 17

3x^4

Answer 18

Almost, it should be \(\sf 2x^4\)

Answer 19

wouldnt u add the X to the 2X

Answer 20

No because we are multiplying not adding.

Answer 21

And 2*1 equals 2

Answer 22

okay

Answer 23

Now, the inside terms are \(\sf 10\) and \(\sf 5\).

Answer 24

15

Answer 25

Remember, we are multiplying

Answer 26

50

Answer 27

Yep, the last terms are \(\sf 10\) and \(\sf x^2\) so what does that equal multiplied?

Answer 28

10x^2

Answer 29

Yep so all together we have \(\sf 10x^2-2x^4+50-10x^2\). The \(\sf 2x^4\) and \(\sf 10x^2\) are negative because in the binomial \(\sf x^2\) is negative.

Answer 30

Now put those in order from the term with the greatest exponent to the term with the lowest exponent.

Answer 31

10x^2-2x^4-10x^2+50 ?

Answer 32

\(\sf -2x^4\) would be first. What is \(\sf +10x^2-10x^2\)?

Answer 33

0

Answer 34

Yep so the final equation will be \(\sf -2x^4+50\)

Answer 35

48x^4

Answer 36

You can't simplify it any further than \(\sf -2x^4 - 50\)

Answer 37

*+50

Answer 38

thts the answer?

Answer 39

Yes \(\sf -2x^4+50\)

Answer 40

thanks for the help

Answer 41

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