Question

factorise (2 x+⅓)² - (x-½)² ​

Answer 1

The given polynomial is of the form a²-b² = (a+b)(a-b)

$(2x+\frac{1}{3} )^{2} -(x-\frac{1}{2} )^{2} \\= [(2x+\frac{1}{3})+(x-\frac{1}{2})][(2x+\frac{1}{3})-(x-\frac{1}{2})] \\= [2x+\frac{1}{3}+x-\frac{1}{2}][2x+\frac{1}{3}-x+\frac{1}{2}]\\=[3x-\frac{1}{6} ][x+\frac{5}{6} ]$

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