need this to be factored (x+1)^2-(x+2)^2

Question

homework.

Also need help with 4x^4 - 1/y^2) (also known as 1 over y squared)

and

9a^2/4a - a^4/b^4 ( also known as (9a squared over 4a minus A to the 4th over B to the 4th

 

Answer 1

By difference of two squares rule,

(x+1)² - (x+2)² = [(x + 1) + (x + 2)][(x + 1) - (x + 2)]

                       = (2x+3)(-1)

                       = -2x - 3

However, -2x - 3 doesn't factor.

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4x⁴ - 1/y² = (2x²)² - (1/y)² = (2x² + 1/y)(2x² - 1/y)

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9a²/4a - a⁴/b⁴ =9a/4 - a⁴/b⁴ = a(9/4 - a³/b⁴)

you can pull out a 1/(4b⁴) if you want and get

a(9b⁴ - 4a³) / (4b⁴) but that's basically it.

 

Answer 2

I'm assuming you want them simplified.

(x+1)^2-(x+2)^2

Is really just 

(x+1)(x+1)-(x+2)(x+2)

For (x+1)(x+1) using the FOIL method we will get: x²+ x + x +1 simplified we get x²+ 2x +1

Same priciple for (x+2)(x+2) we get x²⁺ 4x +4

So we have (x²+ 2x +1) - 1(x²+ 4x +4) I added the -1 because it is understood to be there

We distribute the -1 and get x²+ 2x +1 - x²- 4x -4

Simplify and we are left with -2x -3