How would I find the product for these?

1) (9 - 5x^2).. I think it might be 81 - 25x^2?

2) (x + 2)^3.. I think it is x^3 + 8


3) (2x - 1) (-x^2 - 4x + 3).. Not sure of this one

Not quite right. If you are looking to square the quanity (a+b), you would do the following:

(a+b)^2 = (a+b)*(a+b) = a*(a+b) + b*(a+b) = a^2 + 2ab + b^2.

So the answer to the first one is:

(9-5x)^2 = 81 - 90x + 25x^2.
(note - I think you mis-typed the first question - please verify that the version I wrote here is the correct problem).

For the second one I suggest you first find the square, using the above technique, and then multiply through again by (x+2). You should get an answer that includes terms of x^3, x^2, x, and a number.

For the last problem, rewrite it as follows:

(2x-1) * (-x^2 -4x + 3) = 2x*(-x^2 -4x + 3) -1*(-x^2 -4x + 3)

Then group terms.

Ok, cool. For the second question, I'm guessing that it has to be either x^3 + 6x^2 + 12x + 8 or x^3 + 4x^2 + 6x + 8?

For the last question, I came up with -2x^3 - 7x^2 + 10x - 3.. Is that right?


And one last question.. To factor 6x^4 - 18x^3 + 12x^2 completely, would I get 6x^2 (x^2 - 3) (x + 4) ?

OK - for the second question one of your choices is correct - why is it that makes you unsure? Simply use:

(x+2)^3 = (x+2)*(x+2)^2 = (x+2)*(x^2+2x+4) =...

For the last question your answer is correct- good job!

As for the factoring question - not quite right. You can divide through by 6x^2, leaving 6x^2(x^2 - 3x + 2). The next step is to factor (x^2 -3x +2). Consider the factors of 2 - what two numbers multiplied gives you two? Remember that this can include positive as well as negative numbers. Then pick the pair that add up to -3. You can then write this in the form x^2 - 3x + 2 = (x+a)(x+b), where a and b are the factors you came up with (and may be negative).

Okay, thank you for your help ;)

One last question... If I perform this operation

(-7x^3 + 6x^2 - 11x + 13) + (19x^3 - 11x^2 + 7x - 17)

Do I get 12x^3 - 5x^2 - 4x - 4?

Quote:

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Originally Posted by andyhaus1057

If I perform this operation

(-7x^3 + 6x^2 - 11x + 13) + (19x^3 - 11x^2 + 7x - 17)

Do I get 12x^3 - 5x^2 - 4x - 4?

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Looks correct to me!