## Rkb<3NH 3 years ago The product of (a − b)(a − b) is a^2 − b^2. A: Sometimes B: Always C: Never *is it a?

1. MathBlonde

I think it is B because it would end up being a^2-ab-ba+b^2 Unless there is a zero of course so then it could be A

The product of (a-b)(a-b) is a^2-2ab+b^2 now what conclusion do you think.

3. helpingtutors

so its never hence C

4. Rkb<3NH

it cant be b because i choose it and i got it wrong, but i stuck between a and c

5. MathBlonde

Yes C sorry I got the letter mixed up

6. Rkb<3NH

okay well thank you and can you help me with 1 more?

7. MathBlonde

8. Rkb<3NH

Find the two products below. Compare and contrast, in complete sentences, the similarities and differences of the two. (x + 4)(x − 4) and (x + 4)(x + 4)

9. MathBlonde

the first would play out to x^2-4x+4x-16 leaving you with x^2-16 The second would become x^2+4x+4x+14 leaving you with x^2+8x+14 See the difference?

10. MathBlonde

So the second is +16 not +14

11. MathBlonde

Do you understand how to distribute those types of problems?

12. Rkb<3NH

no im confused?

13. MathBlonde

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14. MathBlonde

the first x multiplies to each term in the second set of parenthesis. Then the first 4 multiplies to each term in the second set of parenthesis. Add all the terms together and you are good to go :)

15. Rkb<3NH

ohh okay! i get it

16. Rkb<3NH

(x + 4)(x + 4) x^2 + 4 + 4 + 16 this is what i get for the second equation

17. MathBlonde

Yes but remember to carry x along. The second and third terms you have just 4. But the 4 multiplies with x making them each 4x So x^2+4x+4x+16

18. MathBlonde

You will be expected to combine like terms as well. So go ahead and add the 4xs together giving you 8x making your final result for that problem x^2+8x+16

19. Rkb<3NH

oh okay can you help me out with the similarities and differences of the two equations?

20. MathBlonde

You can see from our calculations that it is the minus sign that causes the major differences. It turns positive 16 into negative 16 and instead of creating 8x with the 4xs, the 4xs end up canceling each other out because 1-1=0 so 4x-4x=0 as well.

21. MathBlonde

Notice though that both problems do yield an x^2 and a 16(just a negative 16 for one of them)

22. Rkb<3NH

oh yea thats true well thank you soo much, you have been a great help!(:

23. MathBlonde

No problem :) good luck!

24. Rkb<3NH

Thanks(: