Factorise :
4a2−4ab+b2−4x24a^2 - 4ab + b^2 - 4x^24a2−4ab+b2−4x2
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4a2−4ab+b2−4x2=(4a2−4ab+b2)−4x2=(2a−b)2−4x2=(2a−b)2−(2x)2=[(2a−b)−2x][(2a−b)+2x]=[2a−b−2x][2a−b+2x]4a^2 - 4ab + b^2 - 4x^2 = (4a^2 - 4ab + b^2) - 4x^2\\[1em] = (2a - b)^2 - 4x^2\\[1em] = (2a - b)^2 - (2x)^2\\[1em] = [(2a - b) - 2x][(2a - b) + 2x]\\[1em] = [2a - b - 2x][2a - b + 2x]\\[1em]4a2−4ab+b2−4x2=(4a2−4ab+b2)−4x2=(2a−b)2−4x2=(2a−b)2−(2x)2=[(2a−b)−2x][(2a−b)+2x]=[2a−b−2x][2a−b+2x]
Hence, 4a2−4ab+b2−4x2=(2a−b−2x)(2a−b+2x)4a^2 - 4ab + b^2 - 4x^2 = (2a - b - 2x)(2a - b + 2x)4a2−4ab+b2−4x2=(2a−b−2x)(2a−b+2x).
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