math people help!!!?

Question

how can i factor this? can someone please explain it to me in mathematical words so i can understand it mathematically for the test.... here is the question how can i factor (a+1) squared subtract (b-3) squared? please explain in mathematical details in words!!! tyvm!!!

people ya ty great answers ^.^ but um.. its grade 10 factoring o.o; FACTORING not expanding

Answer 1

Try multiplying everything out, then combining:

(a+1)^2 - (b-3)^2 =

(a+1)(a+1) - (b-3)(b-3) =

a^2 + 2a + 1 - (b^2 - 6b + 9) =

a^2 + 2a + 1 - b^2 + 6b - 9 =

a^2 + 2a - b^2 + 6b - 8

Not sure you can go much further with it than that.

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EDITED TO ADD: Answerers #3 (Steiner) and #6 (P.Rutherford) have it! Answerer #3 gave the hint, Answerer #6 did the work. If you want full credit on this homework problem, go with Answerer #6.

Answer 2

Okay (a+1)^2 - (b-3)^2 factored:

Let x = (a+1) and y = (b-3), so we have:

x^2^- y^2 factoring this is simple:

(x+y)(x-y) now get the original variables back:

[(a+1) + (b-3)][(a+1) - (b-3)] simplify

[a + b -2][a - b +4] Voila!

Answer 3

first, since both the terms are squares you can find the square root of the problem. (hint: the square root of a number squared is the number itself) so then you should have (a+1) - (b-3). then since in both parenthesis is just addition and subtraction you can ignore them so you would get a-b+4, because positive 1 minus negitive 3 = 4

hope this helped

Answer 4

Hint: You have 2 squares. How do you factor their difference?

Answer 5

This might help, use FOIL.

First, Outside, Inside, Last.

(a+1)(a+1)

(a*a)+(a*1)+(1*a)+(1+1)
F O I L

Hope that helps.

Answer 6

I am not competley sure but I have an idea.
(a + 1)^2 - (b - 3)^2
change signs
a + 1^2 + -b + -3^2
a+1 + -b + 9
a+10 +-b

Answer 7

If you mean (a+1)^2 - (b-3)^2 then:

(a+1)(a+1)=a^2 + 2ab + b^2

(b-3)(b-3)=b^2 - 6b +9

(a^2 + 2ab +b^2) - (b^2 - 6b +9)

= a^2 + 2ab +b^2 - b^2 + 6b -9

=a^2 + 2ab +6b -9

Answer 8

srry. I'm not good at math.