mathmathmath. FACTORISING. help! ?

1.

Difference of two squares
A^2 - B^2 = (A+B)(A-B)

So

4x^2 - y^2 = (2x)^2 - y^2 = (2x+y)(2x-y)

2.
Factorise into two brackets:

To get 2x^2 as your x^2 term, you'll need to put 2x in the 1st bracket and 1x in the 2nd:
(2x+B)(x+D) = 2x^2 + Bx + 2Dx + (B*D) = 2x^2 + (B+2D)x + BD

Now you need two numbers that multiply to get -15 (B and D). Also, B+2D has to equal -7, to get your x term right. You just need to play around with factors of -15 and see what works when you put them in the brackets! This is what I did, and got:

(2x+3)(x-5)

To check, multiply out the brackets and you get:
2x^2 + 3x - (2*5)x -15 = 2x^2 + 3x - 10x - 15, then collect up the x terms and you get: 2x^2 - 7x - 15.

1. 4x^2 - y^2
=(2x+y)(2x-y)

2. 2x^2 - 7x- 15
=2x^2 - 15 - 7x
=(2x+3)(x-5)

1) 4x^2 - y2 = (2x + y)(2x - y)
This is a difference of squares.

2) 2x^2 - 7x - 15 = (x - 5)(2x + 3)

Good luck in your studies,
~ Mitch ~

2x squared-7xsquared- 15
=2x^2-10x+3x-15
=2x(x-5)+3(x-5)
=(2x+3)(x-5)

Could you specify what is to be done with 4x^2-y^2?

1. (4x-y)squared
2. (2x+3) (x-5)