UGHHHHH

Simplify x(40-2x)(40-2x) over -4xsquared + 1600

If what I have done is what you meant then this would have been the best way to present it.

Simplify         [ x(40-2x)(40-2x) ] / [ -4x^2 + 1600 ]               

I have used difference of 2 squares to factoise the bottom, that is     \(a^2-b^2=(a-b)(a+b)\)

\(\frac{x(40-2x)(40-2x)}{-4x^2+1600}\\ =\frac{x(40-2x)(40-2x)}{1600-4x^2}\\ =\frac{x(40-2x)(40-2x)}{(40)^2-(2x)^2}\\ =\frac{x(40-2x)(40-2x)}{(40-2x)(40+2x)}\\ =\frac{x(40-2x)}{(40+2x)}\\ =\frac{x\times 2(20-x)}{2(20+x)}\\ =\frac{x(20-x)}{20+x}\\ or\\ =\frac{20x-x^2}{20+x}\\\)

Thanks guest, I have only just seen you answer, it was not there when I started :))

NOTE:  The 2 answers are the same. 

Simplify the following: {nl} (x (40-2 x) (40-2 x))/(1600-4 x^2) {nl} {nl} Combine powers. (x (40-2 x) (40-2 x))/(1600-4 x^2) = (x (40-2 x)^(1+1))/(1600-4 x^2): {nl} (x (40-2 x)^1+1)/(1600-4 x^2) {nl} {nl} 1+1 = 2: {nl} (x (40-2 x)^2)/(1600-4 x^2) {nl} {nl} Factor -4 out of 1600-4 x^2: {nl} (x (40-2 x)^2)/-4 (x^2-400) {nl} {nl} x^2-400 = x^2-20^2: {nl} (x (40-2 x)^2)/(-4 (x^2-400)) {nl} {nl} Factor the difference of two squares. x^2-20^2 = (x-20) (x+20): {nl} (x (40-2 x)^2)/(-4(x-20) (x+20)) {nl} {nl} Factor 2 out of 40-2 x: {nl} (x 2 (20-x)^2)/(-4 (x-20) (x+20)) {nl} {nl} Multiply each exponent in 2 (20-x) by 2: {nl} (x×2^2 (20-x)^2)/(-4 (x-20) (x+20)) {nl} {nl} 2^2 = 4: {nl} (4 x (20-x)^2)/(-4 (x-20) (x+20)) {nl} {nl} 4/(-4) = 4/(4 (-1)) = 1/(-1): {nl} (x (20-x)^2)/(-1 (x-20) (x+20)) {nl} {nl} Multiply numerator and denominator of (x (20-x)^2)/(-(x-20) (x+20)) by -1: {nl} -(x (20-x)^2)/((x-20) (x+20)) {nl} {nl} A common factor of (20-x)^2 and x-20 is x-20, so -(x (20-x)^2)/((x-20) (x+20)) = (-x (x-20) (x-20))/((x+20) (x-20)): {nl} -(x (x-20)^2)/((x+20) (x-20)) {nl} {nl} -(x (x-20) (x-20))/((x+20) (x-20)) = (x-20)/(x-20)×-(x (x-20))/(x+20) = -(x (x-20))/(x+20): {nl} Answer: |  {nl} | -(x(x-20))/(x+20)

Oh dear,

I am so sorry guest.

I have stuffed up your answer.  I am very sorry.    

I must have clicked 'edit' in yours instead of in mine by mistake.  I did not even know that I could do that!

I went back to try and fix it but that didn't help.  I don't think I tried to edit it 4 times, not even by mistake.  I do not know what has happened.  I do not know why it has changed it like that either.

I am SOOOOO  SORRY