(x+t)^2 - (x-t)^2 =?

Question

help!

Answer 1

Difference of two squares:
(x+t)^2 - (x-t)^2
= [(x+t)+(x-t)] * [(x+t)-(x-t)]
= 2x*2t = 4xt

Answer 2

(x + t)^2 + (x - t)^2 = 2x^2 + 2t^2 and let us see how we get that.

(x + t)^2 = x^2 + 2xt + t^2 and

(x - t)^2 = x^2 - 2xt + t^2

Simply add the two equations and you see that 2xt terms get cancelled out.

Answer 3

(x+t)^2 - (x-t)^2 =

= (x+t)(x+t) - (x-t)(x-t)
= x^2 + xt + xt + t^2 - (x^2 - xt - xt + t^2)
= x^2 + xt + xt + t^2 - x^2 + xt + xt - t^2
= xt + xt + xt + xt
= 4xt

Answer 4

(x + t) (x + t) - (x - t)(x - t)
x² + 2tx + t² - (x² - 2tx + t²)
x² - x² + 2tx + 2tx + t² - t²
4tx