Math genius needed I am studying for a test tomorrow and have run into difficulty can you please help me?

Question

I need to factor the polynomial.
x^2-y^2
please explain in simplest terms possible.
a^2+4b^2
Here is another one
49y^2-169z^2

your help is appreciated thanks in advance:)

Answer 1

(x+y)(x-y)

already in simplest terms

(7y+13z)(7y-13z)

Answer 2

Remember that the difference of squares always factors into a product of sum and differences: x^2 - y^2 = (x+y)*(x-y). Actually, I think all of these are supposed to be the difference of squares: are you sure the second one isn't a^2 - 4b^2? then the factors would be (a+2b)*(a-2b). The third is (7y + 13z)*(7y - 13z). Learn to recognize perfect squares in this type of problem (difference of perfect squares):

4b^2 = (2b)^2
49y^2 = (7y)^2
169z^2 = (13z)^2

Answer 3

Difference of Perfect Squares:
If you have something that can be written as
[exp1]^2 - [exp2]^2
where [exp1] and [exp2] are any valid expressions, then it factorises as
([exp1] - [exp2]) ([exp1] + [exp2])
So, for instance:
x^2 - y^2 = (x - y) (x + y)

49y^2 - 169z^2
= (7y)^2 - (13z)^z
= (7y - 13z) (7y + 13z)

Now a^2 + 4b^2 can't be factorised. If it was supposed to be a^2 - 4b^2, however, this would be the same as a^2 - (2b)^2, which therefore factorises as
(a - 2b) (a + 2b).

Here's another example:
(3x - 1)^2 - (2x + 3)^2
= ((3x - 1) - (2x + 3)) ((3x - 1) + (2x + 3))
= (x - 4) (5x + 2).

Answer 4

x^2 - y^2 = (x-y)(x+y) --- This is a formula called difference of two squares.

Proving:
R.H.S = (x-y)(x+y)
= x^2 + xy - xy - y^2
= x^2 - y^2
=L.H.S (proven)

U mean a^2+4b^2 or a^2-4b^2?
If a^2+4b^2, then it is already factorized or for more advanced students, = (a + 2bi)(a - 2bi)
If a^2-4b^2, then = a^2 - (2b)^2 = (a-2b)(a+2b)

49y^2-169z^2
= (7y)^2 - (13z)^2
= (7y - 13z)(7y + 13z)

Answer 5

4x+y-11=0 3x-y-3=0 ok take between the equations 4x + y - 11 = 0 sparkling up for y y = 11 - 4x replace it into the different one 3x - (11 - 4x) - 3 = 0 blended like words and sparkling up for x 3x - 11 + 4x - 3 = 0 7x - 14 = 0 7x = 14 x = 2 plug that into between the equations and sparkling up 4(2) + y - 11 = 0 8 + y = 11 y = 3 and x = 2

Answer 6

(x-y)(x+y)

a^2+4b^2 is in simplest form

(7y+13z)(7y-13z)

Answer 7

(x-y)(x+y)
(a+2b) the whole square minus 4ab
(7y-13z)(7y +13z)

Answer 8

(x+y)(x-y)