Question

Factorise 2 x minus 1 by 3 whole square minus x minus 5 by 3 whole square

Answer 1

Answer:

$(2x-\frac{1}{3})^2-(x-\frac{5}{3})^2=(3x-2)(x-\frac{4}{3})$

Step-by-step explanation:

Given : Expression $(2x-\frac{1}{3})^2-(x-\frac{5}{3})^2$

To factorise : The given expression

Solution :

Applying identity,

$a^2-b^2=(a+b)(a-b)$

Where, $a=2x-\frac{1}{3}$ and $b=x-\frac{5}{3}$

Substitute the values we get,

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

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

$(2x-\frac{1}{3})^2-(x-\frac{5}{3})^2=(3x-2)(x-\frac{4}{3})$

Therefore, The factor form of the given expression is

$(2x-\frac{1}{3})^2-(x-\frac{5}{3})^2=(3x-2)(x-\frac{4}{3})$