(a+b) (a+b) (x) (x) - 4abx-(a-b)(a-b)

1.	(a+b) (a+b) (x) (x) - 4abx-(a-b)(a-b)
Answer» We have,{tex}(a + b)^2x^2 - 4abx - (a - b)^2 = 0{/tex}In order to factorize {tex}(a + b)^2x^2 - 4abx - (a - b)^2{/tex}, we have to find two numbers \'l\' and \'m\' such that.l + m = -4ab and lm = -(a + b)2(a - b)2Clearly, (a - b)2 + [-(a + b)2] = -4ab and\xa0lm = -(a + b)2(a - b)2 l = (a - b)2 and m = -(a + b)2Now,{tex}(a + b)^2x^2 - 4abx - (a - b)^2 = 0{/tex}{tex}\\Rightarrow{/tex}{tex}(a + b)^2x^2 - (a + b)^2x + (a - b)^2x - (a - b)^2 = 0{/tex}{tex}\\Rightarrow{/tex} (a + b)2x [x - 1] + (a - b)2[x - 1] = 0{tex}\\Rightarrow{/tex} (x - 1)[(a + b)2x + (a - b)2] = 0{tex}\\Rightarrow{/tex} x - 1 = 0 or (a + b)2x + (a - b)2 = 0{tex}\\Rightarrow{/tex} x = 1 or {tex}x = - \\frac{{{{(a - b)}^2}}}{{{{(a + b)}^2}}}{/tex}

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