Question

Factorise (2x-1)^2-(x-1)(1-2x)

Answer 1

Answer:

$(2x - 1) {}^{2} - (x - 1)(1 - 2x) \\ = (4x {}^{2} - 4x + 1) - ( - 2x {}^{2} + 3x - 1) \\ = 4x {}^{2} - 4x + 1 + 2x {}^{2} - 3x + 1 \\ = 6x {}^{2} - 7x + 2$

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Answer 2

Answer:

(2x-1)^2-(x-1)(1-2x)

4x^2-4x+1-[x-2x^2-1+2x] =0

4x^2-6x+1-x+2x^2+1-2x =0

6x^2-7x+2=0

6x^2-4x-3x+2=0

2x(3x-2)-1(3x-2)=0

(3x-2)(2x-1)=0

3x-2=0

3x=2

x=2/3

or

2x-1=0

2x=1

x=1/2

therefore, x =2/3 or x =1/2